Ideally, I'm looking for a small golf bag with backpack type straps that allow the bag to be a little more upright (kinda like the arrow bags an archer uses). With this, I can pull a few clubs out from my main bag if I just want to go to the range. And the process of getting it packed to go is really fast and simple since I just need to put it on my shoulders. I don't mind the extra weight on my back. I'll be able to bike faster and maneuver in traffic better than if I had a trailer.
The trailer is an option. I would have to be more careful since I'd be hauling something. It'll take time to strap the clubs down properly so that they don't fall out on a hill. Another downside is that it's harder to park the bike since I need to make sure the trailer's not in the way of a path or something. I'd also have to lock and secure the trailer down. A lot of work.
For actually playing a round, I'd have to take my main bag (20-25 lbs) and the pull cart. So I'll likely just use the car. However, one day I might try attaching the pull cart handle to the bike rack and see how that works. It just comes down to how well the attachment works. The pull cart has ball bearing bicycle type wheels, so it should be able to handler speeds up to 15mph.