some drill bits come with hex head attachments on the end, but most inexpensive ones are round, just because the chuck on the drill should be able to hold it.
Now, first question. Are you trying to put these screws into the wall with a regular drill motor? Or do you have like a cordless drill/driver, where you can turn it down to lower speed? Even with a good trigger finger, a variable speed drill motor is a bitch to keep low speed, and really lacks any significant torque to drive screws (unless you've got a BIG drill motor, which then is even tougher to keep at the low speed). If you're using a drill motor, I suggest you beg/borrow/buy/steal a cordless drill/driver, and use that. Generally speaking, I have have had to pre-drill a pilot hole for a screw, unless it was going into hardwood (which generally isn't used for studs in construction of walls).
Second question, are you using drywall screws, or wood screws? Again, better tool to use is a lower speed/higher torque drill/driver. Depending on the size of the screw will depend on a pilot hole size, but going much over 3/32 will probably not leave you enough wood for the screw threads to engage. Even a 1/16 should be adequate (you're only trying to give the screw a path of lower resistance through the wood). Also, you can lubricate the screw threads with some soap (liquid or hand soap....just drag the screw threads across a scrap of soap), and they'll go through the wood easier.
Not sure if that answers your questions or not? :hmm: