I Am trying to understand the psychology here

TALK TO HER TALK TO HER TALK TO HER!!!
I'll tell you WHY it's crucial that you talk to her.
She's your collegue and any rumor spreading on her behalf could hamper your reputation or career growth. I mean we don't even know what the hell she is telling people. So i suggest the following steps:
1. Talk to her

  • Tell her what you told us, regarding why you sent her the proposal, keep it short and to the point.
  • Ask her if SHE has any confusions or questions.
  • Make it VERY clear that you both work in a professional environment, where the focus should be WORK. and the ONLY reason you are talking to her is because you don't want any un professionalism at your work place. *This last line is very important, coz she needs to be clear that you aren't talking to her coz you are in love with her but because you are a mature adult who is career oriented and does not want any unprofessionalism or confusion at work. *
  • Tell her that you are assuming that she has no issues with her and she will act normally
  1. If she continues to be unprofessional and cannot separate her personal stuff from work, you need to talk to your direct supervisor and let him know that you are finding it hard to work with her coz she is being uncooperative/ unprofessional.

bottom line
TALK TO HER.