You may wish to consider renting a magnetic clamp drill or a clamp for your existing drill. Use is self explanatory. You can look at the bit from all angles before you start. It won't move around or get tired. You can focus on the pressure you are using and have a hand free to lubricate the bit.

Performance Tool W3939 2-1/2" Heavy Duty Drill Press Vise - Securely Clamp Workpieces for Accurate Drilling
4.0

Draper Drill Press Vice 70mm | Quick Release Pillar Bench Portable Clamp Vice | Small Mini Workbench Tool | 40390
4.0

Uadme Drill Stand Clamp, Adjustable Rotatable Electric Drill Holder for Holding Power Drills in Any Horizontal and Vertical Position, Practical Aid for...
3.0