If your nervous about falling off, your going to fall off ;)
I've fallen off my green colt about three times. The second time I fell I was especially nervous about getting back on again, as he would do a small rear or start to dance when mounting. I had my dad hold his head while I mounted and dismounted repeatedly, gritting my teeth and just sucking it up while I did so.
I would also work on your hands while on the ground and then while in the saddle. Work on picking them up quietly and releasing (don't let go entirely!) just as efficiently. Practice *not snatching* the reins if something startling happens (like a spook).
I did that with my poor little gelding, he tripped in a hole and my head went down with his neck. Unfortunately, I didn't release the reins like I should have (allowing for a free head and mouth) and yanked on his mouth. That head came right back up and smacked me right in the nose, causing me to fall clear off the horse!
He was fine (no mouth or leg damage, but that snatching DID cause excess pressure and probably some pain!). I got right back on again and we went along our way.
A snatch at the mouth or sudden kick to the ribs because of your instinctive reaction to a spook can cause a horse to suddenly buck, because all of a sudden YOUR the predator and they want you off.
Desensitizing work with a flag on the ground can also help your mare become more confident in unusual situations, such as working in an outdoor arena alone or with a friend. Put her on a long line and simply work on touching her with the flag. Wave it around, rub her all over with it, etc.
A spooky horse will want to bolt clear back into yesterday, but if you remain quiet and patient they WILL calm down and WILL accept this new, scary object.
Do not get loud, excited, or nervous, as that will come off onto your horse :)
Wait! I'll fix it....