Practising against or just out from a wall will probably help. You might also want to consider rolling out of your handstands rather than bridging. It is probably safer. A common problem is sticking out your head and arching your back. You should be very straight in your handstand with toes above hips, above shoulders, above hands. You should be looking at your hands but with your eyes not your whole head. Your neck should be craned back. Practise standing with your arms above your head, pressed in to your ears, and look up at your hands but keeping your neck fairly neutral. It sounds silly but beginners get very confused being upside down.
When you are in your handstand you have to squeeze the muscles in your core and legs very tight to stay nice and straight. If you lose tension you'll lose you'll your balance.
That happens to me all the time when I get lazy and relax :) I was told to tighten my core and my friends told me to kind of grip the floor. I don't know but it worked for me :p anyway, you can also practice doing handstands against the wall so you can get the feel of it and so that your muscles can remember and become stronger :)
Squeeze all your muscles.
What I do is if I feel like I'm going to go over, I bend my arms and I usually go back down.
Hope this helps :)
I do them on a trampoline. Make sure tht when you're falling you move urself.
