Just some things to think about;
I would use Brownell's AcraGlas Gel bedding kit. With the black dye that comes with it, it should match up pretty good.
I would wrap tape around the barrel to get the free float. It can be sanded later if more is needed, but I would get a good barrel channel shape by using tape.
I would tape the top of the stock and use lots of the release agent fluid, that comes with the kit......everywhere.
I would allow barrel contact on the bottom for 1'' out from the receiver for stability.
And of coarse, I would also bed the action if it is not already, and probably do that first in a separate first step. Then do the barrel channel. Doing both at the same time would be too much for me to keep track of all at one time.
I might have to buy 2 kits depending on how much filling is needed.
http://www.brownells.com/.aspx/pid=1038/Product/ACRAGLAS_GEL_reg_