If you're looking for a free package that you can fiddle with to get an idea in your head of what you're after, I've found this to be reasonable.
http://www.openscad.org/
One thing about it is that it's a programming language. You model the components of the bike piece by piece and use binary operations/transformations to combine the pieces or put them in place.
I'll admit SolidWorks is nice, and the open source world is yet to come up with an interface that's as intuitive. I've been fiddling with OpenSCAD though for building a bicycle trailer and so far I've been able to model a lot of detail.
The wheels shown are modelled off the Giant SXC2 wheelset I have spare. A downside to SolidWorks is there isn't an easy way to generate 2D plans, but given you can spin the model around in 3D space, you can then turn to a 2D CAD package and re-draw it out, having gotten the model pretty much figured out.