I am going there in the middle of February. I prefer to stay in Fort Davis, which is about 1 hour of so from Big Bend. It is at a higher elevation, so it is a bit cooler. It can get to the 20's at night in early March but near the park which is lower in elevation, you can easily get into the low 80s by then. Unless you dual-sport, the two fun rides near Big Bends is the "River Road" or park road 170 from around Terlingua to Presidio and the "Enchanted Loop" - starting in Ft. Davis, take 118 then county road 166 and back to Ft. Davis. On the Enchanted Loop there is the McDonald Observatory. The Observatory is equipped with a wide range of state-of-the-art instrumentation for imaging and spectroscopy in the optical and infrared, and operates one of the first and most productive lunar ranging stations. At night they have a Star Gazing party using the large telescope. Caution: riding back to Ft. Davis will put you on some really deer intense roads after the Star Party, so be careful.
It's 145 miles from Ft. Davis to the Park HQ so it's a bit
more than an hour but it's a nice ride, especially once you get south of Alpine on 118 - lots of nice fast sweepers.
The Star Party is a great thing - my two boys were absolutely gobsmacked by the Milky Way from horizon to horizon - they grew up in the NE so the really dark sky is not a normal thing for them. I've been to at least a dozen Star Parties and never get tired of the experience.
Concur on the deer after dark. Find a caravan of cars and ride in with them. My wife and I made the ride from Ft. Davis to Alpine after a Star Party...it's a long ride at 20 miles per hour but the freaking deer are so thick that to ride any faster would be suicide.
Good eats at The Reatta (pricy) in Alpine and for breakfast I like Alicia's (cheap).