dude, i f you want to use your own rig, you should. i've played a million of these gigs with 3/4 other bands, and always bring my own rig (previously Ampeg 810, now 2 swr goliath II's).
i have no problem whatsoever telling folk they can't use it.
the best reason i ever heard why i should let 3 other bands use my rig was 'if everyone brings their own gear there will be arguments over who wants to use what'. funnily enough in 15 years of gigging i've yet to have that discussion...
make it clear you're bringing YOUR rig, and no-one else is using it. I emphasise; make this absolutely transparent.
Offer your cabs - no-one else will bring a head anyway...
if they all turn up with their own rigs, then i'm sure everyone will have no problem with tagging together a bass super-rig!