Back to this topic again after a while! In the end I stuck with the Zoom B1 but haven’t totally gotten along with it. With the new NAMM announcements there’s 2 more products that are looking interesting for that simple home practice setup.
Vox VGH-Bass - looks like a new version of their old amPhone product, all self contained with a pair of headphones and just plug straight into the bass. It’s a bit lacking in details so far as to what effects etc. you get with the bass version, but might be a nice practice solution? Downsides seem to be needing AAA batteries, and only aux-input (no bluetooth)
Fender Mustang Micro - now this looks neat. A more modern version of the old amplugs, and though it seems quite guitar focused, it did mention “fitting most guitars and basses” so I assume it has something for us too. The major plus for me (if it works as advertised) is that they claim to have bluetooth streaming with audio/video syncing, which was the main reason I didn’t keep my NUX mighty plug. Perhaps not as customisable as the NUX due to no app, but if the presets are good enough this might be a winner?