Use a semi-hard wood for making the bow drill's spindle and fire board. A good indication of the hardness, is if you can indent the wood with your finger nail. If possible use the same wood for both the spindle and fire board. Woods like cedar or willow work well to make a bow drill's spindle and fire board.
The hand hold for a bow drill should be a hard wood or material (sea shell, bone, hickery nut, antler, or even a rock (not ideal), bottle cap, canteen lid, metal cup). Best to have as little friction as possible so you can spin your spindle as fast and smooth as you need to get it past the 750 degree heat that you need to make a coal. You can lubricate the hand hold or top of the spindle with oils from your face (along side your nose). Don't get it wet though, as that will cause the wood to bind up and grab.
Here are some of the best woods for making a bow drill spindle and fire board:
• Cedar (Eastern White Cedar)
• Staghorn Sumac
• Willow (Most Willows)
• Balsam Fir
• Aspens and Poplars
• Basswood
• Spruces