It's possible to recover if the player before you bids 6 in this situation, especially if it's an early round. Bidding 7 usually is a bad idea, because that just validates their decision to bid 6. If you dump it on the 6 bidder, now you'll have more chips than them for the rest of the game and can get bargains.
A lot of people, after winning a 6 bid like that, pass immediately on the next round to save their chips. That usually gives back any gains from the previous round.
Unfortunately, this is a game where you sometimes lose due to other people's bad decisions. You wind up in a hole if the player before you overbids, but you can recover.