I think the pillar drill suggestion above is a good one. Steel can work harden if the drill bit starts to rub rather than remove material.
A pillar drill will help apply sufficient downward force to keep the drill bit cutting.
And again as already suggested, use drill bits that increase in diameter in small increments, rather than one large drill bit to do the whole job.
If the bolt is stainless steel, work hardening is certain to happen with even the slightest of rubbing rather than cutting. Anyways, good luck
