I’ve been playing bass for many years, and I’ll generally echo the sentiment so far: you don’t generally need much in the way of effects when it comes to bass.
I’ve usually got a tuner and a delay and that’s about it. If my amp didn’t have channel switching and a nice overdrive, I’d have a distortion of some sort. If I was playing reggae at all, I’d get an autowah/octave divider/envelope filter of some sort.
I’ve never been a fan of compression pedals, chorus or flanger on bass, and reverb really does just muddy that instrument up. So, I don’t recommend those.
If the SWR lacks anything, it’s tubes. If you want to keep its headroom while getting somewhere near the B-15 tone without having to shell out the money for a SVT, you could get a tube preamp. A good one will give you nice smooth compression with a little bit of pleasant distortion. Prices on them vary greatly, from $50-crazy, and they all have a different character, so be sure to play through it before you buy one.