SalmonCubes

I'm not entirely tech savvy when it comes to hardware of any kind, so I thought I might ask all you good people for some help.
I've been playing bass for a little over 6 months now, and I have been using a small, 25W Peavey 110 Bass Amp. It's served me consistently well, haven't had a single issue with it so far. However, I have recently been invited to join a local band. I have checked with the other people in said group, and it seems as though I would be entirely drowned out in live performances by the guitar amps. (Both are over 60W.)
I'm now looking for a new amp to bolster my sound, and for a somewhat good price (under $350.) What would be a good option for this? I'm looking for a long term amp system that can be loud when I need it.
Also, a (probably stupid) question: Since my amp is 25W, would a 300W amp be able to be essentially 12 times louder? How would the sound quality differ in these two, particuarly with a low B string?