On tiny bits like that I use a pin vise and drill by hand. Start with just 1/4" of the bit sticking out of the pin vise and drill till the pin vise jaws meet the work piece, then pull the drill bit out of the hole (VERY gently) and extend the drill bit another 1/4" and extend the depth of the hole. In twoor three goes, the hole is through. A little picky but generally the drill bit survives the encounter. Pin vises, laddy - that's the ticket.