If you want more distortion, you want to overload the input of the 12AX7 tube. You can do that by adding another amplification stage in front. Some so called high gain amps do this with another 12AX7.
Depending on your amp, the 12AX7 stage might be able to be modified to provide more gain. A simple option for you is to add an effects box. Instrument -> effect box -> amp input. I use a Bass VT pedal to do this but there are tons of distortion pedals out there. Check out the effects
newsgroups on TB, in particular this
thread has a lot of info.