I've just gone cover to cover in the 1690/1691 Apollo's Banquet and there is no Bear's Dance in it.

Here are the contents, for those who don't believe me. In The Third Part of Apollo's Banquet numbers 52 through 68 are not in numerical order--they must have been bound wrong. They are shown below in the order in which they were bound:

Apollo's Banquet: containing Instructions, and Variety of New Tunes, Ayres, Jiggs, and several New Scotch Tunes for the Treble-Violin. To which is added, The Tunes of the newest French Dances, now used at Court and in Dancing-Schools. The Sixth Edition, with new Additions.   In the Savoy: Printed by E. Jones, for Henry Playford at his Shop near the Temple Church, and at his House over against the Blue-Ball in Arundel Street in the Strand, 1690.

1. The New Canaries
2. A New Jigg
3. A Northern Jigg
4. Mr. Banister's Jigg, or, The Altitudes
5. A Jigg, divided twelve ways
6. Inner Temple Jigg
7. Middle Temple Jigg
8. Lincolns-Inn Jigg
9. Grays-Inn Jigg
10. Wat's Jigg (?)
11. The dance in the Play of Macbeth
12. A Theatre Jigg
13. Parthenia
14. The Simerons Jigg
15. The Dancing Horse
16. A Theatre Tune
17. The Opera
18. The Earl of Sandwich's Farewel
19. Captain Digby's Farewel, or, Carman's Whistle
20. A Theatre Dance
21. Captain Hollis's Farewel
22. The Hobby-horse Dance
23. The Gun-Fleet
24. The Prince of Orange's Delight
25. Mr. Farmer's Magot
26. Come Boys fill us, &c.
27. Sawney
28. Fy, nay, prithee John!
29. Philander
30. A Scotch Tune
31. A Scotch Tune
32. A Minuet
33. A Theatre Tune
34. A Round O
35. A Theatre Tune
36. A Theatre Tune
37. A Theatre Tune
38. Minuet
39. Bread of Gad
40. Young Jemmy
41. Could Man his Wish Obtain
42. Old Simon the King
43. A Horn-pipe
44. A Theatre new Tune
45. A New Scotch Tune
46. The Tune of Farrinel's Ground, to the Song of ( All Joy to Great Caesar)
47. Where would coy Aminta run?
48. Jenny, come tye my Cravat
49. Now the Tories, &c., or, Royal James
50. State and Ambition
51. The Gold-ring, a Theatre new Song Tune
52. The Knot
53. Ham House, or Cherry Garden
54. The King of Poland
55. The Mug-house
56. Prince George's March
57. Duke of Grafton's March
58. A Minuet
59. The Scotch-man's Dance in The Norther Lass
60. A Passingalia
61. New Seranade
62. Duke of Bucelugh's Tune
63. A Minuet
64. Kingsale; a new Tune
65. Hedge-Lane
66. To bed we'l go
67. A Scotch Horn-pipe
68. The Shoe-maker, a Scotch Tune
69. A Scotch Tune
70. A Scotch Tune

The Second Part of Apollo's Banquet, containing several new Tunes of French Dances for the Treble-Violin and Flute, performed at Court, and in Dancing-Schools
1. An Entry
2. Saraband
3. La Beauford
4. Saraband
5. Saraband
6. The Galliard
7. Corant: Sen. Baptist
8. Minuet Dolphin
9. Bore Versaille
10. New Bore Versaille
11. Bore Angletar
12. Bore Portuguese
13. Bore Madam
14. La Princess Royal
15. La Fountainbleau
16. La Duchess
17. Minuet Royal
18. Minuet Baptist
19. La Madam
20. Minuet St. Andrew
21. Minuet
22. La Princess Orleance
23. Minute: Round O
24. Corant
25. Minuet
26. Minuet
27. Minuet
28. Corant
29. Corant
30. Paspe
31. New Bore Baptist
32. Minuet        
33. Bore
34. Bore
35. Round O
36. La Bell Princess
37. New la Monmouth
38. Bore Baptist
39. New Provo
40. Corant le Reyne
41. La Modena
42. La Catherine
43. New la Monsieur
44. La Princess
45. La Princess Ann
46. Minuet
47. The New Provo
48. Corant la Grand-Britain
49. La Ben Cavalier
50. New la Dolphin
51. La Prince
52. New la Duchess
53. Bore le Reyne
54. La Buchan
55. La Doncaster
56. New Bore Paspe
57. La Delphie (?)
58. La Monmouth
59. Corant de la Force
60. The Brauls
61. The new Brauls
62. The Brauls, by Monsieur Peasable
63. Corant
64. Bore
65. Saraband
66. Minuet
67. A Seranade
68. A Scotch Tune
69. A Scotch Tune
70. A Scotch Tune
71. A Scotch Tune
72. A Scotch Tune
73. A Scotch Tune
74. A Scotch Tune

The Third part of Apollo's Banquet, containing several of the newest Tunes of Dances for the Treble-Violin and Flute, now in use at Court and in Dancing Schools

1. A New Entry
2. A New Ayre
3. Minuet
4. Long Cold Nights
5. Second Part of Bread of Gad
6. A New Scotch Tune
7. A Scotch Tune by Mr. Dyer
8. A New Scotch Tune
9. A New Scotch Tune
10. The Northern Lass
11. The Banditti; a Round O
12. A Jigg
13. Mr. H. Purcell's Jigg
14. London Ladies
15. In a Desart in Greenland
16. A New Bore
17. Hampton-Court
18. A Farewel
19. Minuet
20. Paspe
21. The Ann
22. Corant
23. Bore
24. The Princess
25. Minuet
26. Tricatrees
27. Minuet
28. A New French Dance
29. A New French Dance
30. Minuet
31. Minuet
32. Rigadoon
33. An Entry
34. Minuet
35. Minuet
36. Paspe
37. Bore
38. Minuet
39. Minuet
40. An Entry
41. Minuet
42. A New Italian Ground
43. Tom Morecock
44. Mr. Mountfort's Delight
45. Lilli Burlero
46. A new Tune
47. Cesacho's Farewel
48. An English March, by Mr. Akeroyde
49. Horn-pipe
50. Horn-pipe
51. Why is your faithful Slave disdain'd
63. Medburn's March
64. Clowns Dance
65. Vulcan's Dance
60. I Often for my Jenny strove
61. A New Rigadoon
62. Minuet
52. The Emperour of the Moon
53. A New Tune
66. Clowns Dance
67. Round O
68. A New Tune
57. Fairest Work of happy Nature
58. Sabina in the dead of Night
59. Sylvia now your Scorn give over
54. A New Posture Dance in Dr. Faustus
55. A Scotch Minuet
56. How quick a Wit
69. A New Theatre Tune
70. A new Tune
71. Round O

Apollo's Banquet: containing variety of the newest tunes, Ayres, Jiggs, and Minuets, for the Treble-Violin, now in use at publick theatres, and ad dancing-schools, being most of them within the compass of both of the flute, and flagelet, to which is added some new songs and catches. The Second Book. In the Savoy: Printed by E. Jones, for Henry Playford, and are to be sold at his shop near the Temple Church, and at his house over against the Blue-Ball in Arundel-Street in the Strand, 1691.

A new Catch.

Choice New Tunes, Ayres, Jiggs, for the Treble-Violin.

1. A New Warlike Tune of Mr. Courteville's
2. A New Playhouse Tune of Mr. Montfort's
3. Oh! how happy's he!
4. A New Scotch Tune of Mr. Courteville's
5. A Minuet
6. Valiant Jockey
7. A New Playhouse Scotch Tune of Mr. Montfort's
8. A Minuet
9. Celia, that I once was Bless'd
10. For Iris I sigh
11. A Scotch Tune
12. The first Ayre of Mr. Finger's
13. The second Ayre of Mr. Finger's
14. The third Ayre of Mr. Finger's
15. The Sages of old, in Prophecy told
16. A Minuet
17. A Round O of Mr. Tollett's
18. An Ayre of Mr. Tollett's
19. A Minuet
20. A Minuet
21. A Round O.
22. An Entry of Mr. Frank's
23. A Minuet of Mr. Frank's
24. Mr Purcell's Scotch Tune in Aphitrion
25. Mr. Purcell's Tune in Amphitrion
26. A Tune of Mr. Purcell's in Amphitrion
27. A Tune of Mr. Purcell's in Amphitrion
28. A Tune of Mr. Purcell's in Amphitrion
29. A Round O of Mr. Peasable's
30. A Paspe of Mr. Peasable's
31. An Ayre
32. A Boree
33. A Paspe
34. The City Ramble
35. An Ayre of Mr. Courtiville's
36. An Entry of Mr. Courtiville's
37. A Trumpet Tune
38. A New Trumpet Tune of Mr. Keller's
39. A New Tune of Mr. Keller's
40. A Round O of Mr. Keller's
41. A New Trumpet Tune
42. An Ayre of Mr. King's
43. Make your Honours, Miss
44. A Minuet of Mr. Tollett's in the Play of Love for Money
45. A Minuet of Mr. Tollett's in the Play of Love for Money
46. A New Tune of Mr. Tollett's in the Play of Love for Money
47. A Tune of Mr. Tollett's in the Play of Love for Money
48. A New Theatre Tune of Mr. Tollett's in the Play of Love for Money, or the Boarding-School
49. A New Theatre Tune of Mr. Tollett's in the Play of Love for Money
50. A New Theatre Tune of Mr. Tollett's in the Play of Love for Money
51. A New Round O
52. A New Tune
53. A New Theatre Tune of Mr. Purcell's
54. A New Tune of Mr. Purcell's
55. A New Hornpipe of Mr. Purcell's
56. A New Theatre Tune of Mr. Purcell's
57. A New Tune of Mr Purcell's
58. A New Trumpet Tune of Mr. Courtiville's
59. A New Minuet of Mr. Courtiville's
60. A New Tune of Mr. Montfort's in the Play of The Greenwich Park
61. A New Tune of Mr. Montfort's in the Play of The Greenwich Park
62. A New Scotch Tune of Mr. Montfort's in the Play of THe Greenwich Park
63. A New Tune of Mr. Montfort's in the Play of The Greenwich Park
64. A New Tune of Mr. Montfort's in the Play of The Greenwich Park
65. A Dance in the Play of All in COnfusion
66. Mr. Tollett's Clowns Jigg
67. Budro, an Irish Dance
68. A New Saraband of Mr. Banister's with the Ground-Bass
69. A New Boree of Mr. Banister's
70. A New Hornpipe
71. A Minuet
72. A new Song, set by Mr. Barrincloe
73. A new Catch in the Play of The Knight of Malta. Set by Mr. Henry Purcell
74. A new Song. Set by Mr. Montfort.
75. Bacchus's Health: To be Sung by all the Company together, with Directions to be Observed.

A New Addition to the Second Book of Apollo's Banquet
1. A Dance in the Play of the Boarding-School
2. A Tune in the Boarding-School
3. A New Dance
4. What shall I do, &c.
5. Fairest Ille, &c. [This and the four following Tunes in the Opera of King Arthur]
6. We've cheated the Parson
7. Come if you dare
8. How blest are Shepherds
9. Thou doating Fool
10. A New Scotch Tune in The Wife's Excuse
11. Still I'm wishing, &c.