How to get a broken torx bit out of a bleed screw?
From the photo you posted reasonable option is to drill a hole in the bit and use drill extractor, spinning it anti-clockwise.

Bit is made of hardened CrV steel, so drilling it may be hard, since it should be precise and centered. If you feel unsure about your skills, give it to professionals, to locksmith or to your local bike service. It may appear cheaper, since damaging caliper housing would be much more expensive than spending some extra euros to have it fixed.