Fastest Way To Cook Bottom Round Roast
You can cook bottom round quickly, but not as a roast.  


Cut into thick about 1 to 2" (2.5 to 5 cm) thick, with the grain.  (depending on thickness, either split it in half / thirds / quarters ... you just want them of similar thickness), cut them thinner if you like it more towards medium than medium rare)
Salt, and let it sit out to come up to room temp for about 30 min.
While waiting, adjust oven rack so the steaks on a broiler tray will sit about 1" (2.5cm) from the broiler, or pre-heat your grill (if using propane ... if you're on charcoal ... well, you really need a chimney starer, or take a propane torch to 'em to get 'em going well in a short time)
Start heating the broiler (only takes 3-5 minutes, typically)
Pat dry the steaks, both sides.
Broil for about 6 min per side; if griiling, might have to go a little longer, depending on how hot your grill gets.
Remove from heat and let rest for about 5 to 10 minutes.
Slice thinly across the grain into strips.
Toss with whatever spices (cumin, garlic, etc.), squeeze some lime over it.


You can get extra flavor into it, but don't use a dry rub.  As we're going for high heat, if you want extra flavor, after cutting your steaks, pierce them liberally with a fork or one of those spiky meat tenderizers (not the mallet ones), then toss in a bag with a marinade, (a mix of lime juice and italian dressing works pretty well for mexican applications, as it's pretty quick.  Worcestershire or soy sauce also work for just about any treatment).

You still want to pat them dry, or else you risk causing the steaks to cook unevenly  (the edges evaporate first, then curl up holding in the liquid ... but the curling places them closer to the broiler and the liquid means the middle can't get above 100°C, making the edges char way before the middle's cooked).

update : and to make sure I'm clear on this -- it's very important that you slice the strips in the end thinly, and across the grain.  That's the only thing that's going to keep it from being overly chewy with this technique.  (and keeping it fairly rare; otherwise it could start to get tough).  Don't bother w/ slicing diagonally if it's going into tacos or burritos (as that's mostly to make it look like a thicker steak), it'll be more tender if you slice straight across.  If you insist on cooking it to medium or further, I'd heat up some salsa or other flavorful liquid in a pot, and drop the cooked sliced strips in there to cook 'em a bit further without it drying them out)