twitter bootstrap is great to get started and its exactly what it intends on helping developers. Instead of creating a lot of stuff from scratch, you got pretty much everything you need for a basic-to-medium frontend so you don't have to worry about it.
As you build your application, there will be times where you would need, for example, to replace the color of the buttons. So instead of having a .btn-primary be blue you want it pink.
you can override the .btn-primary in your own css, or even better, see how it behaves, copy the styles, change what you need and use your .pink-btn-primary.
Little by little your css would stop being twitter bootstrap and become your own variation, with the ability to rely on features being added to bootstrap with time.
Relying on bootstrap has a bit of a shortcoming - if a bug is fix or a new version changes its behavior (rare on css, but very possible on js) you will have to adjust to make sure you get the behavior that you want.
Also, You should be careful, as suggested, not to use their class names, and make sure you load your css files after bootstrap files.
good luck.