I finally have enough enthusiasm for the 3rd phase of our basement remodeling which includes moving safes to a new position and bolting them down.

  How do you drill a fire resistant safe?

  I'm pretty certain it's concrete lined so do you start with a high speed twist drill, switch over to masonry and back again?

  Thanks for you wisdom!

I'd bet it has holes in the floor

Yep, I bet the mount holes are already there so mason bit and hammer drill with concrete anchors.

Bottom is soft a drill will go right threw drill like you describe.

What model safe? Some safes that are fire resistant have a badass concrete and ceramic matrix. It would be very difficult to drill into the base of those safes.
How much does the safe weigh and what size is it?

I should have mentioned it's going over flooring so into floor joists and, I'm hoping, a couple in the rear to the wall studs.  I'm pretty well stuck with placement so the floor holes are unlikely to match up with floor joists.

  It's a cheapy Liberty safe that's probably around 400 pounds.  That's the reason I want to secure it as well as possible knowing I'm only buying time for some tweaker that really isn't professional.

  It'll be sandwiched in between two other safes and we're blessed to live in a low crime, rural area so I'm comfortable with the risk I've assessed.

A cheaper safe shouldn’t be a problem to drill holes for bolts. You really don’t need anything special. That’s just cheap sheet metal that’s not hard. A metal drill bit will go right through it.

Cheaper safes often use fire-rated drywall for insulation.  You shouldn't have any trouble drilling that, and the steel shell, with a standard HSS drill bit - just keep the RPM low and pressure high.

My nephew's driving here Friday to help me move the safes and put up a couple of partitions so it'll probably be next weekend before I have the safes in place so I'll post how the drilling went.

  Thanks for all the replies!