Jim- the same version is in American Memory:

Betsey Baker

From noise and bustle far away,
Hard work my time employing;
How happily I pass'd each day,
Content and health enjoying.
The birds did sing, and so did I,
As I tradg'd o'er each acre,
I never knew what 'twas to sigh,
Till I saw Betsey Baker!

Li too rol, &c.

At church I met her dress'd so neat,
One Sunday in hot weather,
With love I found my heart did beat,
As we sung psalms together;
So piously she hung her head
The while her voice did shake, ah!
I thought if ever I did wed
'Twould be with Betsey Baker.

Li too rol, &c.

Now from her side I could not budge,
I'm sure I thought no harm on't,
My elbow then she gave a nudge,
And bid me mind the sarmont;
When church was over out she walk'd,
But I did overtake her,
Determined I would not be baulk'd--
I spoke to Betsey Baker.

Li too rol, &c.

Her manners were genteel and cool,
I found on conversation;
She'd just come from a boarding school
With a finish'd education.
But love made me speak out quite free--
Says I, I've many an acre,
Will you grant me your company--
I shan't! said Betsey Baker.

Also from American Memory there is a version that says the tune of Betsy Baker was used for the "Quilting Party:"

Betsy Baker/THE QUILTING PARTY

As SUNG BY R. H. RACEY. -- AIR: Belsy Baker.

It was down at Major Parson's house,
The gals they had a quilting,
Just for to show their handsome looks,
And have a little jilting.
There was Deacon Parson's daughter Sal,
Squire Wheeler's daughter Mary,
And General Carter's youngest gal
That looked just like a Fairy.

There was Lucy White and Martha Brown,
And Jackson's daughter Betty,
Femimo Pinkhorn, Prudence Short,
And Major Downing's Hetty.
But if there was a handsome gal
That would make a feller's heart right,
I guess it was, by all accounts,
Miss Carolina Cartright.

O, as they were a whirling plate,
And playing hunt the slipper,
Jerusha Parson's went to git
Some cider in the dipper;
But just as she had left the room,
And got into the entry
She gave a scream and stood stock-still,
Just like a frozen sentry.

We all run out, and there, I swow,
Both huggin' like creation:
Miss Cartright and Sam Jones we saw
A kissing like a tarnation.
O, such a laugh as we sat up,
You never heerd a finer.
Says I, I reckon kissing's cheap,
Don't you Miss Carolina?

You ought to see Miss Cartright blush,
Just as if she'd fainted;
She said she had the toothache,
And in Samuel's arms had fainted.
Now, all young gals, I'll say to you:
When you go to a quilt-make,
Don't let the fellers hug and kiss,
Unless you've got the toothache.

Both songs seem to have the cadence of "Yankee Doodle." There's another reference to a quilting party but it's a different song:
"Aunt Dinah's Quilting Party" that has become a bluegrass song.

-Richie