Step 2Prep the cap
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Carefully determine the proper drill bit diameter to use. If you have calipers or another accurate way to measure then use it. But I don't. I tend to rely on the rack that my drill bits came in to approximate the right size bit. Of you can hold them up to each other and eyeball it. Or put the drill bit and pen on a level surface (check with your level first) and with them close to each other - perhaps an inch or two apart. Then put the level on and make sure it is still close to level. In all cases you actually want the drill bit slightly smaller than the pen.
If you have a vice you can try putting the bottle cap in it. Or adjust a set of locking pliers (Vice-Grip type) so that they will hold but not crush the cap. Or screw it onto the bottle and bravely drill the cap while holding the outside of the bottle. I, of course, would prefer that you find some safer way to do this though.