wood is fine... but one thing you have to focus on is not allowing the board to move at all when drilling... I broke some bits when I first started because i let the board slip a little when drilling... you have to hold it securely.
also, it does require the drill press to have a decent spindle... if it is wobbly or otherwise unsteady it will break bits. the drill press I currently have is a dremel attachment, however it is almost worthless because it is rather poorly made so it deflects noticeably when going up and down, and is just generally unsteady. I just ordered a higher-quality drill press stand from minicrafttools.com, I can't wait to get it.
also, you need to try to run the bits at high speed. you have to remember, these bits were run at like 60,000 to 120,000 RPM's on high-speed drills when they were used in industry, so they are not designed to run at low speeds. the dremel is capable of 30,000 RPM's, which is a lot better than the 2,000 or 3,000 RPM's you'll get out of most regular drill presses. I have noticed that at the speed of the dremel, the bits go through the board like butter, and don't break from non-sideways forces, whereas with the regular drill press I used to use, they would sometimes just break randomly during normal drilling even when I was careful about side forces, due to the low speeds.