As noted previously, Bower with regard to shelter or plants has several meanings, most of which were in the English language by the 1400s or before (OED); Old English from Teutonic roots:
1. a dwelling or abode (in print by AD 1000).
2. an idealized place ("dear lovely bowers of innocence...").
3. a covered stall or booth at a fair.
4. a chamber in a large house or building.
5. a boudoir or lady's apartment.
6. a lady's attendant.

7. a place overarched with branches.
8. a shady recess, a covert.
9. a large nest.
10. a shaded run, for animals.
11. "The bower that wanders in meanders, ever bending, Glades on Glades." Addison 1706.
12. "Care must be had that you do not confound the word bower with arbour, because the first is always built long and arch'd, whereas the second is always round or square at Bottom, and has a sort of dome or ceiling at the top." Bradley Family Dictionary, 1727.
13. Branches of a tree.
14. To enclose (in a structure).

Bower. In the meaning of farmer, a husbandman, a tenant who rents a herd of cows, etc., was in use in English from the 15th century or earlier, but is now obsolete (From Ger. bauer of Dutch bouwer, as noted before).