In the situation the OP has described - from my POV the genders do not make a difference as the issue is general appropriateness rather than predatory behavior.
Bessie is repeatedly asserting, in social settings, that she is close friends with OP, a view which OP does not share and for which the history of interactions (limited initial in person contact, followed by friending then de-friending on FB) would not support most folks making such an assertion - and Bessie continues despite OP's gradual cooling of behavior to Bessie when they are incidentally present at group events.
While Bessie's general inappropriateness extends to also repestedly stating her crush on OP's husband, she is not overtly pursuing him - so I would put this into a category of additional annoying behavior more in line with Bessie making other unwelcome "admiring" comments coupled with the starting point of overstating her relationship with OP.
Someone who I did not know well, and had felt "guarded" about from first interactions would annoy me if, on future chance encounters, they continually proclaimed to others present that we were close friends, and added any further comments which would - perhaps - be taken in a close friend "joking" manner if we *were* close, i.e. "I just love how she puts herself together, I am going to make her my personal stylist!". But my annoyance would be with the overall comments, not just one particular part.
My mother will comment on my boyfriend being handsome, and I could imagine her joking, on seeing him clear a table after a family meal "oh, it is so attractive when a good looking man clears the dishes!" or something in a similar vein, which i would not find offensive or harrasing, nor do i think my boyfriend would. Comments and the reaction to same are not based solely on reading a parsing of the words, but generally are read also for tone, and - when they are of a personal nature - the context of of the parties relationship.
What I would find annoying, and possibly offensive about Bessie's iterative comments is the totality of assuming/stating a closeness which not only does not exist, but for which I had given ample social cues that I did not want to pursue. It would not be less bothersome, to me, if Bessie stopped stating a crush on my SO, but substituted a different repeat statement which also assumed and put forward an appearance of a close relationship which did not exist.
So, in any statement I might make to Bessie to directly clarify matters, were I aiming to revise her behavior towards me/SO, I would not address solely her "crush" and related comments, but the full scope of the inappropriate comments. Focussing only on her crush on OP's husband could suggest all other comments Bessie repeatedly makes are just fine. Of course, if OP is annoyed only by Bessie's crush, addressing only that could work.