I'm going to slightly counter brildum's statements and point out that I was unable to stay on a bouldering climb for something like six months after I started top-rope climbing. I just didn't have the strength (less important) and skill (more important).

Admittedly, I have known a few people who've gone straight into bouldering and pulled it off. Give it a try. If you can, great.

By the way, one of the best things about rock climbing is the social aspect. You should look at partnering as an opportunity rather than a hindrance. I've made a lot of good friends at the gym over the years.