Any wood stocked bolt action rifle I own gets pillar blocked, epoxy bedded, and free floated. I have often heard legends of free floating or bedding jobs making accuracy worse, but after bedding hundreds of rifles, I can say I have NEVER seen one get worse, so if you show me a real-life bolt action rifle which shoots worse after pressure relieving work was done, I'll show you a piss-poor bedding job.
Bedding jobs don't necessarily stop the action from moving during the shot (they kinda do), but rather proper bedding jobs help ensure the actions are seated in the stock the same way for every shot.
Anyone can do a block & bed job. Not everyone can do a good one. If your smith is experienced, then have them do it. If not, then have someone else do it. The method for measuring your results is easy, but most folks don't own a mag base dial indicator to measure it. It's very hard to screw up a bedding job, and very easy to improve accuracy, at least slightly, even with a half-assed bedding job, but it's not something EVERYONE should do for themselves. Remington actions are easy, Rugers are not. A guy needs to be sure he can sink and bed the pillars true to the action bore line to prevent contact with the screw shanks, so either piloted counterbores or drilling fixtures (either stock mounted guides or stock holding fixtures mounted in a press) should be used. I use the following spectrum - if you wouldn't change your own oil, I would recommend you do NOT bed your own rifle. If you can change your own oil, but wouldn't tackle changing your own water pump, bedding your own rifle probably still isn't for you. If you're the type who might build your own shed, retile your own bathroom, or change the headgasket on your truck on your own, bedding is a cake walk.