Prout09,
The inside tapering diameter of your trumpet should be something like this,,, at the beginning smaller portion of the taper 1/8 - 5/32 inch in diameter, at the larger exhaust end of the taper 1/2 inch in diameter. This tapered portion should extend aproxiamately 3 1/2 inches. The tapered aperature should be as gradual as possible from the smaller end up to the larger 1/2 inch end. When you are ready to begin drilling the blank out mark the dead center of one end of the blank. Afterwards insert the blank into the chuck on the lathe with the previously marked end facing towards the opposite tail piece end. Position the blank in the chuck so that it is as perfectly straight as possible and tighten it firmly in place. Insert a long 1/8 inch drill bit into the chuck on the opposite tail piece end. Be sure the tip of the bit will start precisely into the previously marked dead center of the blank. Drill the pilot hole all the way through the blank with the 1/8 inch bit. Now you're ready to begin drilling out the tapered portion. Also, especially if you are using one of the very dense woods like Blackwood or Cocobolo be sure to frequently back out the drill bit and pick out the wood filled flutes of the bit. This may not be the best way to do this but it is a way I have found that works well for me.
Ron