Well, what are YOU doing when she does this?
Chances are, you are encouraging her behavior because things like this usually are the rider's fault (unintentionally), with the horse just responding accordingly.
First thing, make sure your saddle is adjusted properly and fits her properly. If anything is pinching her or uncomfortable, the force you create when you try to get on could really be hurting, thus causing her to move to get away from it.
Are you kicking her in the side when you put your foot into the stirrup? You may be accidentally cueing her to walk if you are.
Make sure to hold your reins in one hand with the slack taken out of them when you are mounting so you have control if she does decide to start walking forward.
If she does take off when you get a foot into the stirrup, freeze EXACTLY how you are and pull back on the reins to stop her (this is why you have your reins ready to go in-hand). And then ask her to back up a few steps. Allow her to stand quietly after that. If she does so, finish mounting and allow her to stand and relax for about 10 seconds (at least), as standing quiety is her reward for correct behavior. If she does not want to stand still, then back her up again a few steps at least. Again, give her the opportunity to stand still. If she does, mount the rest of the way. If she doesn't, guess what? We're backing up again.
When you do get on, are you letting her walk off right away or do you make her stand for a few seconds? You should be making her stand for a few seconds or more whenever you mount, and do not let her walk off until you give her the cue to do so.
This issue has absolutely nothing to do with you and her "having a connection". It is about you taking the control and being the leader of your little herd of two. And to be aware of any and all cues you are sending her, either intentionally or unintentionally.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.