Hi Chris,
Good luck with the surgery! I can't really comment on side of bed, as I stayed on the same side (right leg to the floor) for surgeries on both hips, two years apart. My experience was that getting in and out of bed was the most painful thing post-surgery, but I can tell you what worked best for me. These recommendations are for the first week, or two, depending, and longer if need be.
First, I only got in and out of bed once a day. Definitely limit the number of times you get in and out of bed. Keep the pee bottle they give you, for use at night, especially. You have a recliner; put it in the bedroom, or at least on the floor that you will be sleeping in, to limit stairs during the first few days, week.
If you have one, a bed rail can be very helpful, but not a requirement.
As I said, I stayed on the same side of bed (so can't comment left vs right) but the single most important trick I discovered regarding anything post-surgery was to get in and out of bed from the bottom. For me, the invisible dog-leash they give you to rope your foot didn't solve the pain problem getting in and out of bed, as at some point in the procedure the leg moves from side to side (which the strap doesn't control for) and that was the cause of the really great pain.
Bottom of bed technique: sit on bottom of bed, as far back as you can get. Lay your upper body back on bed and use your arms and good leg to worm your way up bed. To get out do the same thing in reverse (though you might need the strap more in getting your foot to the ground, can't remember exactly).
Best of luck,
Mike