You should be honest and tell her.
A few years ago my neighbor put his house up for sale. The house sold, but not yet closed. One day we were in our yard when a realtor drove up and then another car with a young man, the both went into the house next door. We did not think anything of it since the for sale sign was still in the yard.
About 10 minutes later, my neighbor drove up, came over and we chatted for a few minutes, then we said something about the showing of his house, he looked a bit surprised... walked over to his house, went in, and to his surprise, there was the young guy on the floor letting the realtor enter the back door.
Needless to say this freaked him out and he went off on them doing the dirty in his house. Turns out the realtor had a wife and children at home but also liked men and would often do this in houses that he knew were sold. How would this guys wife feel if she didn't know he was bi?
Would you want something like this to happen to your new friend years down the road?
Be honest and tell her the truth even if she leaves. Not telling her is selfish and dishonest on your part.