BIN is a great primer if there is no varnish, shellac or urethane over the stain of your wood. If there is, XIM or Brunning's "Grabber plus" will give much better adhesion to that type of surface. You should know that if there isn't a clear coat on the wood, the stain will bleed through XIM and but won't bleed through Grabber.
A one coat process can't be done here. You need a primer to bond and provide a sealed surface for the paint to adhere to. If you attempt to use paint with no primer, you'll be sorry in a few months when the paint begins to chip and peel.