Should I bed the rail and install rings first before I bed the action. I was thinking that installing the rings and rail after bedding the action could cause some minor bending of the action and induce stress.
Sounds like a chicken or the egg question. It doesn't matter. The whole purpose of bedding is to reduce/eliminate stress. So if you bed the action correctly, torque it in place properly, then correctly bed the rail, no stress will have been produced. Same thing goes the other way around.
Bed the action stripped of any optics or rail. It will be stress free . Check rail fit then if it needs bedded do it. It is stress free now. If u use good rings and a good base and every thing was bedded proper, the rings won't need to be lapped .