If volume is going to be an issues then I'd personally go for an NUX Mighty Plug, just the cheaper first version rather than the newer, more expensive one. That should leave nearly £250 for a bass.
Very briefly the NUX plugs into your bass with headphones then plugged into the NUX, leaving you free to roam if you feel so INCLINED. The NUX is recharged through USB and you download a phone app which let's you set up seven presets with amp models, effects etc on each preset. You can bluetooth your phone to it to play along with wherever you get your music from.
Sounds technical to a noob but it's really intuitive and will let you try out all sorts of effects. It sounds very good too where most of the cheaper 'amp plugs' dont.