It's a pedal like any other. It takes a signal, processes it, and spits it out the other side. It doesn't matter what that signal is. A volume pedal is pretty much a volume pot, like the one on your bass. I'm sure some do (in the way of buffers) effect tone etc, but they are designed to just move the volume up and down, as such I'd be surprised if you notice any tonal change regardless of what you put through it!
I own an Ernie Ball VPJnr and have owned a Morley one and also a cheap Bespeco one. I've used all three with bass, and with keys and guitars in the studio and noticed absolutly ZERO change in tone between all 3 of them on all instruments. The only difference, as with all volume & expression pedals is in what feels comfy to you under foot.
Many pedals come in different types and with different pots (25k etc). Someone else correct me here, but as far as I was concerned, such details make no difference when the pedal is used as a volume pedal, but do when used as an expression pedal as different equipment requires different resistance. When used as a volume pedal, it is effectively an 'effect' pedal, sat in-line with other pedals and so (as is my experience), in this capacity ALL volume pedals function perfectly well with ALL instruments.