Most standard guitar wahs will remove the guts of your tone when you tread on them. There are bass specific wahs but, like the Dunlop, they tend to affect a particular set of frequencies rather than the full sweep of a guitar wah.
A notable exception is the Ibanez Weeping Demon - it has guitar and bass settings, but even with the guitar setting you can keep the low end thanks to the EQ control. The guitar setting SCREAMS with bass, and with a fuzz is instant Cliff.