I've been there right after Christmas the past two years. Best time to be there. Highs from the 60s to about 80 are typical. I've ridden from Furnace Creek out to Badwater and Artists Drive. Maybe 35 miles round trip to Badwater. No problems whatsoever. Little traffic, good road. I don't remember any bike rental places, but I wasn't looking for one either. Taking plenty of water is a good idea even though it probably won't be excessively hot, if for no other reason than there is zero water available in many areas out there. No need to get carried away though, especially for the kind of relatively short out-and-back riding you're describing. It's not as though you will be in the middle of nowhere where nobody can help you if needed (like off-road backpacking or something). There are plenty of [car] tourists going from one attraction to another to help, in the unlikely event you were to really get desperate.
I met someone on a Pacific Coast tour a couple of years ago who finished up her tour by riding through Death Valley on her way to Las Vegas. Her blog is
here. Scroll down the page for the table of contents. Death Valley stuff is near the bottom. Note: It's in German, but look for the italics for her English translation.