How does it shoot?
I have had quite a few guns that shot great bolted straight into the bedding blocks with no bedding. If you bed the stock it lowers resale value of the stock. I always recommend that with bedding blocks or chassis that people shoot them without bedding and if they shoot good then don't touch it.
Look at the number of top competitors in PRS and even F class that are using alluminum chassis. They are the same mating design generally as the bedding block and they are a proven method.
Every once in awhile bedding will help a gun shoot better, but I think that is the exception and not the rule.
All that being said, if you are already set on bedding then I personally would do the whole action. If I am going to the trouble of taping stuff off, applying release agent, mixing epoxy, etc., then I would rather just do the whole thing. It isn't that much extra work and it would put my mind at rest about if my half-assery was affecting my precision or not. I tend to think it is unlikely to make much of a difference one way or the other.