Whether there are any pipes embedded in the concrete depends on building style & type of building. Usually, in a North American house built of wood on a concrete foundation, the foundation and slabs are poured after the drain/sewage and water service entry since they have to be below the frost line, and everything else is completed afterwards. A slab is usually 6in thick, and the top of pipes underneath it may touch the bottom of the slab.
So look around the basement, trace all water, gas and electrical lines: if it's underground and embedded there will be an exit/entry point somewhere.
That's the speculation part. Now to the specifics of your question:
How do I determine whether pipes (water, electricity, gas) are buried in basement concrete?
- obtain building drawings. These may be available from previous owners or the city
- perform a concrete scan. There are specialized services that perform just that for any drilling: they look for gas, water, electrical, other plumbing, rebar and tensions lines, which are common in concrete structures.
is there much safety to be gained from drilling 1mm, vacuuming, and inspecting, before drilling again?
If you puncture or scrape the pipe or jacket it's too late. So unless you know it runs in a sleave this approach is not effective. This might work if you have better visibility and for that you should use a wider drill bit. Also requires a degree in archeology.
will be used for a (bicycle) floor anchor
Unless you are close to the exit point of such a line, which you would see, it is very likely that the lines are at least 1in buried. SO you could roughen up the concrete, and add a cement build-up for the anchors. Or use adhesives for a wooden base, and screw into the base.