A/B switching.

A bypass looper and a DI at the amp will do nicely. I like the Boss LS-2, it performs this effects loop function well and can do other useful things, is well built and is reasonably priced, especially used.

 

As stated by @spufman.
LS-2 would be fine but does a lot that you don't necessarily need.
I'd use one of these :
Loop Pedal Switchers - - 1 Looper (Micro, LED Version) - Loop-Master Pedals
And put more money for a good DI to place at the very end of the chain (I personally use a cab sim -Omnicabsim- that has a DI out for that purpose, since I find the pure bass tone to be too clinical for my taste).
Signal chain would be bass > looper in > looper send > effects > looper return > looper out > DI > amp + FOH
Would that work for you ?

 

One of the Radial Engineering mixer/switcher products might work, especially if you're willing to DI out of your amp.

 

^^^This. Signal goes from bass > loop selector > DI > amp. When you step on the loop selector it adds all of your other gizmos into an effects loop that returns back to the loop selector before continuing to the DI. Easy-peazy. I like the semi-custom loop selectors available from Loopmaster but there are lots of products that take this same approach.