Don't grip on a horse ever! They feel every muscle of yours and it affects everything. If you are scared of bouncing off, get off of your horse and continue the ground work, and find someone that has a very mellow horse and practice bareback walking with long loose legs and a halter. Or take up lessons.
By you gripping, not only are you setting yourself up for a bumpy uncomfortable ride, but you are making riding with you not fun for your horse and they're learning to take every inch you give them (loosening reins) as an opportunity to get away.
It's okay to be nervous, but keep your body relaxed :) When you ride, release all of the tension even before you get on. Hand walk the horse and make sure YOU are nice and relaxed. Stretch before you ride, that also helps to relax.
It's going to take some time, but don't think "oh I'm going to fall off!" because that puts you into a panic and gets your muscles tightening and your horse will feel that and they won't feel safe.
When you ride, your eyes map the way infront of you, your body will follow.. your horse will too. The biggest thing that helped me to relax was first relaxing myself and erasing the "what if I fall" or "what if he bolts?!" or other what ifs from my head. Also, getting lunged by a riding instructor on different horses because it helped me to adapt to different kind of walking and trotting. Then when I got back to my boy, he and I were both pleasantly surprised and there weren't problems anymore :)
Adding onto what some have said above, after you get on does your horse just start moving on their own or do you ask?
If they start moving, make them ho. Ask with a little pressure and increase until they do, then release (I'm sure you know :P)
If you ask, make sure you breathe in deep and focus on every muscle letting go and being relaxed. Even your wrists need to be relaxed, your face (so many nervous riders make the craziest faces..) you need to remember to breathe!! It's easy to forget when you focus hard on other things. Your ankles and toes, your calves , your THIGHS and knees , everything :)
Best of luck!!!