Get all of the grease off of the bolt. Wipe it down throughly with a rag soaked in Gunscrubber. Put maybe one drop of oil down the firing pin hole, and that's all.
Buy some dry lube (its a graphite-like, powdered substance,that you can get at any gunstore), and put that on the bolt if you feel like it needs lubrication.
I'm almost sure that this will solve your problem.
If it doesn't, then a good military Mauser 98 action, or Springfield action (don't use a 1903 Action, use a 1903A3 action, these were made only during World War II and don't have the heat treat issue of some of the early Springfields, and they are cheaper). These both have a somewhat wobbly bolt (when the bolt is fully to the rear), in order to make them more realiable in dirty, gritty conditions. You don't need to built a sporterized rifle in one of these actions. Go to a couple of big gun shows, and you will find several of these sporterized rifles for sale, and much cheaper than a new rifle. (Sporterizing these rifles was very very popular in the 1950s, and there are lots of them still around.) But, these rifles can be somewhat heavy.
Hope this helps.
Mannyrock