You're just as likely to get to 390 as to bust, say, since you give up a bit of advantage to the house.
Betting $10 is fine strategy. Your risk of ruin is [to me] acceptably small, and you aren't going to waste too much time wagering. Then again, I'd say the same ting if you bet $50/hand, which is likely what I'd bet.
For risk of ruin, check out
http://wizardofodds.com/blackjack/appendix12.html. your case is 250 hands, and you began with 20 bets, so your risk of ruin should be between 20 and 30%, about 27%.