Simply raising the volume wouldn't cause pumping without a compressor somewhere, which you didn't really mention. Not all compressors are born equal, and they all have a range of settings that give a range of sounds (for example a mastering limiter set to auto-release will sound completely different to one set to a fixed release.) Some high end compressors / limiters can compress more with less noticeable pumping. You can't change the mix of the track... but mastering can never change the mix of a track.
Anyway, a multi-band compressor may fair better. A single band compressor on a master bus is going to have fairly macroscopic effects.
Also, compressors in serial with the right settings can achieve more transparent results.
Separate mid-side compression can also have good effects on the presence of a track without altering peak levels.
These things require experience I think. I have no idea what level of experience you have with compression, so enter at your own risk.
NOTE: if the source material you are messing around with is less than 24-bit then compression is going to introduce quantization distortion which you might or might not want. If its pumping it may well simply be that the bass thunk is too loud. You might find a roll off of the bass to be enough to reduce pumping while keeping the dynamics you want. Try different things and A/B them. Get some reference material to compare to as a sanity check.
