If you're mainly talking about jamming along with tunes and learning new material, etc, then here's where I'm at...
I used a Tascam CD-BT1 for YEARS... I've gone through two of them. The one I have now has thousands of miles on it... I use it almost every single day and I have learned HUNDREDS of songs on it. It's small, has some neat features and is easy to use. You can slow down tracks while retaining pitch, loop, and tune... however, the sound quality is not the greatest.
HOWEVER...
I am all about embracing technology and recently discovered a kickass app for my iPad called "Anytune Pro" and it works exactly like the CD-BT1, but pretty much WAY better in almost every possible way. It has superior looping functions that you can save to a track, you can import MP3's from your iPad or iPhone or even connect to your home network and do it that way. Slowing down the tune sounds WAY better than the Tascam, and there are a TON of cool EQ features for isolating bass or any other instrument. It's a quality app, and the iPad version is only $15.
Here's a demo video for the Mac version:
https://www.youtube.com/watch?v=plgry6gyE_oAlong with that, you'd need some kind of interface to plug your bass into your iPad or Mac and there are tons of those available... If you're looking for a compact, no-frills solution, I've heard pretty good things about the iRig HD, as it works really well with bass. I'm shopping right now for a new one... if I find something good, I'll let you know.