I was just making use of the word: bit.
Ed H has presented info regarding quality HSS steel. You won't rapidly wear out good quality drills when using a good cutting lubricant.
I'm more particular about a clean drilling area, than about drill cutting edge temperatures. Rust and dirt can can dull cutting edges. I think you're using new steel, so that shouldn't be much of a problem with this project. Beware of hard spots in cheap materials such as OBF old bed frame angle iron. Hard spots can occur in new stock, but they're fairly uncommon. Hard spots can quickly wipe out the cutting edges of a sharp drill.
It may be useful to use a cutting lubricant dispenser bottle, like a poly lab-type wash bottle. These bottles don't need to be tipped upside-down to dispense liquid, making them very easy to use for cutting lubricants because they don't distract the user from the operation of the machine. The spouts on the wash bottles easily direct the cutting lube to the actual cutting area.
With a handy dispenser, you can keep drilling instead of letting up on the feed pressure. A small amount of cutting edge rubbing can take place as a drill is allowed to retract from the cutting area during drilling.. this rubbing is more detrimental to the cutting edge than heat, IME.
Once good chip flow is achieved, I generally keep the drill cutting all the way thru.. while adding small amounts of cutting lube to the hole with the dispenser bottle in my other hand.
Eventually, the drills are going to need sharpened, so be on the lookout for the type of tools or equipment you'll want to use for sharpening.
There are a lot of good fixtures and sharpening machines available. Developing a reliable hand sharpening technique with a bench grinder is about the lowest cost method available.