If you really want to go to town on the bass sound, try combining a miked amp with one of the DI techniques described earlier. Often you can get away with a smaller amp than if you rely on the amp sound alone, as the DI will provide all the bottom end you need. This combined approach is taken by many professionals. The relative phase of the miked and DI'd sound has a profound effect on the final result, so you may need to phase-reverse one of the sources to get the best result. Also, experiment with the EQ of the individual sources as well as their balance, as the EQ controls may not have the same effect as they do when the sources are heard in isolation. Similarly, changing the mic-to-speaker distance will also affect the phase of the combined sounds, so this can be useful in fine-tuning the result.
As you can see, there are several ways of recording the bass guitar, but if you like to keep your options open until the final mix, there's nothing wrong with DI'ing the bass flat via a DI box, perhaps in combination with a limiter to catch any excessive peaks, then applying one of the techniques outlined here at the mixing stage. Or if you have enough spare tracks, you can record the processed and the clean version of the sound on different tracks. I'd certainly try to do this if I was miking the amp -- all that's needed is a DI box between the instrument and the amp (most have an audio thru connector) with the DI out connected to a spare recorder input. Computer users also have several options open to them when it comes to treating sounds after the event: in addition to the usual compression and EQ, there are now numerous software amp simulators that can produce very convincing results. The beauty of the home studio is that you don't have the same time pressures as a commercial facility, so you can afford to experiment and see what method works best for you