What are the notes of a generic bass line for a blues in B minor? Should one just play the notes of a B minor chord?
Typical blues bass lines follow the chord tones, whether major or minor. Here with Bm blues, on the B bars, use B D and F. Since it's blues, the m7 also comes into play. So that's 1,3,5,7 from the Bm scale. As extra passing notes, the other three from the scale will also work.
Going to Em, usually in bars 5 and 6, use the same numbered notes, but from the Em scale.
In minor blues, the third chord can be F# (maj. or min) or I have played G7. Again, 1,3,5,7 mainly, with 'stepping stone' notes of 2,4 and 6.
That covers it! Use all the notes! And for a bit of extra spice, most of the chromatic in between! The one avoid note on the Bm bars will be A#...and D# on the Em bars. Although that D# works fine as the last note on a Bm bar, before an Em bar.
You need more than a collection of notes to make a good walking bass line. Good bassist don't just meander about on arpeggios. Some just play the roots and it can sound pretty good if the rhythm is interesting. If you really want to learn how to construct a walking bass line over changes (Blues included) I would recommend the following...
Listen to blues tunes you line and figure out the bass line by ear, or find tab for it. This will give you an idea of how bassists think.
Get your hands on books like Evolving Upward by Rufus Reid or something similar.
One frequently uses voice leading, aiming for specific notes on strong beats, to create smooth motion. This doen't mean that you must be smooth, you could slap and pick octaves, etc. To this end you need the full set of changes to work with. Are you doing a 12 bar minor blues or an 8 bar pattern? Without this info we really can't help you. But as Tim points out you do have more than one chord and the standard 12 bar blues goes something like this...
I -> IV -> I -> I -> IV -> IV -> I -> I -> V -> IV -> I -> V
This is not the only pattern but a simple starting point. A minor version of this might be the same with all minor chords. Most Jazz players would make the I and IV chords minor and keep a dominant 7th on the V for a proper resolution. If your blues tune moves to other chords then staying on Bmin would clash horribly at some point.
You will need more than a
A common minor blues...
i i i I7 iv iv i i VI7 V7 i V7
Bm Bm Bm B7 Em Em Bm Bm G7 F#7 Bm F#7
You could simply arpeggiate the chords as you suggested, normally play the chord root on beat 1. Lots of blues method provide bass patterns so try browsing through those. Keep in mind that blues piano methods often include left hand bass parts. Some will involve chords that probably cannot be played on bass, but many will be playable on bass.
"What are the notes of a generic bass line for a blues in B minor? Should one just play the notes of a B minor chord?"
Well, you'll want an Em7 chord as well, and you can choose between F#m7 and F#7 for the third basic chord. Given that framework, you have the same popssibilities as with a major blues. Keep it simple, we're talking about a bass line, not the bass solo!