If all else fails:
Even so, I wouldn't attempt it with anything less than a brad point drill bit. For trem posts you can get away with a few degrees of 'not vertical-ness'. The more critical components to the drilling process for the bridge is the absolute positioning on the face of the guitar for both posts and ensuring the holes don't become ovalled out while you drill, something that I peronally wouldn't trust to a regular twist drill bit, even using a drill press.
The use of a guide, above, should get you within acceptable tolerances on the vertical and roundness of the holes as long as you go carefully. The positioning of the two holes is entirely down to your accuracy of measurement and placement of the bit, which TBH is something you still need to be mindful of when doing this operation in a drill press anyway.
At the end of the day, you work within the boundaries of the tools and skills you have available at your disposal. Use the partscaster as a learning experience and a stepping stone for the next bigger thing.