#1 thing to do is believe in yourself and convince yourself that you can do it without your coach. This can be done by picturing yourself doing it perfectly without your coach when you're not at practice. I still do this when I tumble, and I am a tumbling coach. Warmup really good too. If you aren't warmed up, that does not help AT ALL.
Do you have a cheesemat that you can do your backhandspring on? When I have girls that are scared to do their bhs by themselves, I first have them do it on a cheesemat. I'll spot them at first, then they'll feel comfortable to do it by themself. I gradually tell them to move a few inches down the cheesemat, then throw their bhs. Eventually you're on the end of the cheesemat throwing your bhs by youself! This was how I overcame my fear of my bhs years ago, and it is the most successful technique with all of my tumblers. Literally once you throw it by yourself at the top of the cheesemat, you're set for the bottom. :)