Thanks for the advice Gareth, unfortunately there's no mute option on the amp for tuning. I'm now thinking of using two LS-2s before and after the tuner...
Two basses into the first LS-2, set to switch between two inputs one output to the tuner, then out of the tuner into the second LS-2, having this one set in reverse to the first, one input two outputs, onto both channels of the amp. That way I can tune either bass with no interference to the gig.
I know it means having to hit two pedals when I want to change bass, but I think it should solve the problem.