I have... briefly. Sort of.
I had an earlier BB800 with a defective component that caused the noise levels to ramp up to unusable levels after it was turned on -- this happened over a course of anywhere from 10 seconds to several minutes.* While I didn't get to gig it in the short while I had it, in messing around with it (in its well-behaved stretches) at home through my MAS 112, I found a lot to like and suspect that a properly working unit would be fun to play on a variety of gigs.
*I should note, again, that my head was an early one. Quilter Co. were responsive in communication (Pat Q. and an associate both responded to me and tried to help me troubleshoot the amp before I sent it back) and they have, as far as I know, long since tracked down and rectified the issue with the defective component (which was not an issue in the majority of early amps).
Overall, I liked the feel of the BB more than that of the Peavey Minimega and the Genzler Magellan I tried around the same time. Both of those amps were more open up top (which I liked) and had more versatile EQs than the Quilter (and the Peavey had more going on in the deep lows and the Genzler had probably the best slap tone), but the Peavey felt stiff by comparison and the Genzler (to me) felt compressed in its lowest register. The BB, as I recall it, felt nicely elastic and propulsive with a balanced response/feel through the registers of the instrument. Big but not bloated lows and, yeah, some "heft" (more than a lot of compact amps, but not as much as my favorite lead sleds).
Played back to back with a Shaw B-150 tube amp (150 Watts, four KT88s) and my GBE 1200, I did
not feel that the BB800 had the same level of solidity and detail -- the Shaw, despite its tube power, felt and sounded more crisp, more detailed, and more articulate -- though I'm sure the Quilter would go louder -- but I did find the overall sound of the Quilter to be pleasant and fairly organic (harmonics spoke nicely without being zingy) and the overall feel to be more natural and "connected" than the majority of class D bass amps I've tried. I wouldn't characterize it as a super "quick" amp -- relative to the GBE 1200, it could get a little blurry in fast, staccato stuff -- but it was still nicely responsive. An easy amp to play, if that makes sense; for me, the feel encouraged a relaxed right hand technique (except when trying to play fast, sharply delineated lines at
my limits -- the GBE was better for that).
If the BB's positive qualities held at gig volume (which, again, I didn't get to try), I think it would've worked well with my MAS 112. The EQ, while limited, I recall as being well-voiced -- add a presence knob or a well-voiced bright switch and I'd have been more than happy with it. As it was, I would've liked it a bit more open up top, but it was still a very usable gig sound with good mids. The feel was a hair looser than I prefer (possibly related to its having a lower damping factor than most SS bass heads); the flip-side of that is that it's probably the closest approximation, in terms of feel, to a tube amp that I've played in a compact, class D bass head -- nice, natural note-envelope and, again, a feeling of connectedness to what you're playing.
Don't recall if I tried the DI.
Overall impression: Wouldn't replace my fave lead sleds or pre+power rigs and maybe not the best amp if you're looking for a very bright or open top end or a super-quick feel, but would be a great backup/easily portable head with a more natural feel than the majority of compact, class D bass amps I've played. If mine didn't have an issue, I'd likely have kept it. If they came out with a version with a bright switch/presence control or something similar -- especially if they revised the DI and included a selectable damping factor -- or just slightly tightened up the feel -- I'd very likely get one.
Seemed to match up well with my MAS 112 (which is solid in the lows but voiced pretty "lean and mean"). Not sure how it would match with a deeper, slightly looser, more "romantically" voiced cab like the 46 -- might be too much of a good thing for me (then again, I like things fairly tight and responsive -- might be just right for some). Again, I never got to gig the head.
Re. using the BB with Markbass cabs (per the OP), while I am no expert on them (I own a CMD 121P combo and have played a few of the others), they seem to me like they'd benefit from a fairly tight, controlled head -- not sure the BB800 would be a good match and I could see the combo being "rubbery" -- but that's a subjective impression involving some guesswork.
@Mike Arnopol has remarked favorably on the BB800 -- he'd probably be able to speak better to how it pairs with his cabs than I could.