Bullet has a very well-working collision pipeline. They support various broadphases (sweep n prune, hashed broadphase, 3-axis sweep, etc) and have narrowphase with optimized bv-tree's. I've worked professionally with bullet for over a year and although their performance is not as good as havok(which I've worked with for over two years), it's free and the source code is maintained and enhanced often.
It should be fairly easy to look into their source-code to figure out how to only use their collision detection.
PhysX also has a collision-detection network but I haven't relly looked into it. Havok is a solution that costs a lot of money and I don't think anyone can afford retrieving their source-code unless you're a professional developer. They do have free-to-use libraries but then you can't modify it.