Steel isn't that bad.
You using a drill press or a hand drill? Either way, clamp it. Trust me, you don't want that thing catching and spinning on ya.
I dunno how thick the small bear stuff is...is it mild steel, galvanized, cold rolled, stainless? Regardless, cutting oil is always helpful and will prolong the life of your bits. Tap magic is great, but smells like cancer. Pleasant cancer, if you're into gasoline, but still...there's plenty of great options out there. I'm trying to go a little more eco-friendly recently...
Use a sharp bit. Step bits are great. You'll actually find it's easier to keep a drill bit on target in steel if you have it started correctly.
If you're having trouble with it, your bit might be dull, or your drill might be underpowered if it's struggling at the larger sizes.
Different materials react differently. The hole saw that chewed through galvanized steel at high speed will be reduced a pathetic circular nub disc after a few seconds on stainless.
The best overall advice I can give, drilling through ANYTHING: keep things cool. Heat is what softens and dulls the cutting edges of your drill bit, lube that thing up and if you're having a hard time, keep the speed low and go a little bit at a time.
And don't assume that a harder bit will always perform better, either. With increased hardness you get increased brittleness...though this applies for thicker materials: there's nothing worse than getting a broken drill bit stuck in a hole.
Well...maybe a tap..