Hmmm, I suspect I've been lucky. As much as I hate to admit buying
them, I found the "Bullet" bits to be damn good for this job.
I just used a standard drill, set to a low speed and ensure that the
hammer setting is off.
I start very slowly until the drill has 'bit' and then I increase the
speed slightly and apply quite a hard pressure.
If at any time I think the drill bit is getting too hot then I just
back off (go for a cuppa) and then start again.

The life of the "Bullet" bits when used this way isn't great, but
they're not that expensive....

Seri