Most headphone amps and mixers are designed for mic or line sources and don't have a high impedance input suitable for direct connection to a passive bass. Those Behringer mixers people posted earlier ([url="http://basschat.co.uk/topic/277361-behringer-ub802-mixer/"]I'm selling one![/url]) fall into this bracket. You [i]can[/i] just plug in a passive bass but the tone will suffer as a result. Do you have an active bass, or a pedal you can use in between?
If not then get something specifically marketed as a guitar/bass practice unit. I have a PJB Bighead and cannot fault it, there's one used on here right now but at £110 it's probably more than you want to spend:
[url="http://basschat.co.uk/topic/279189-phil-jones-bighead-headphone-amp/"]http://basschat.co.u...-headphone-amp/[/url]
The Vox Amplug is a cheap solution - make sure you get the bass version, and there is a an improved v2 out now too (which also means v1 versions are cheap as chips on eBay).
The Zoom B1on is about £40 and has a headphone amp, aux in, tuner, drum machine, looper, and 100 FX, which is stupendous value. However the headphone amp is not powerful enough to drive the higher impedance headphones that are commonly used in studios. It was OK with my earbuds but quiet as a mouse when plugging in the big cans.