Being a Seattle burner, I've done this drive lotsa times and lotsa routes.
How big and heavy your vehicle is plays a part (I go awfully heavy!).
Yes you can do it in a day, I'd say in just an Explorer without a trailer it wouldn't be that hard. I used to do it in a Ford F250 with a camper and a trailer in a day. It's a long goddamm day.
In recent years I've found making a two-day trek is lots better for several reasons. No matter how well you pack, you're gonna want to make stops at stores on the way for stuff.
The other biggie is that if you do it all in one shot, you arrive in BRC late at night and very tired. If you're not in an RV, it sucks to have to immediately set up camp.
You'll also learn to enjoy the stops along the way because you'll usually meet other burners doing the same thing. They're easy to recognize! They'll be driving a truck with mannequins and fur and REALLY odd stuff sticking out, and bicycles tied all over it.
As for route, I've learned to favor I-5 down to Eugene, then across HWY 58, then down to Klamath Falls, then Aturas - Cedarville - PLAYA!
When you roll into Alturas, there will be a Chevron at the main intersection. Stop there. They know who you are and where you're going, as does the general store across the street, and they're glad to have you. That Chevron has an RV dump where you can get rid of any waste water on the way back, and the general store has a garden hose out back so you can fill up on all the water you want on the way in. Just down the street is a liquor store with great California prices, cheaper than Washington.
From Alturas to Cedarville is Cedar Pass, 6300 feet, be nice to your vehicle going over it! DON'T leave it in "Drive" and floor it all the way up the pass. Shift down and let up on the gas and walk it up easy so nothing (like your transmission!) overheats. It's not that far up, and it's REALLY important to NOT break down way the hell out there. Even if you are doing the one-day thing, it's better to go easy up Cedar Pass and make sure you ever get there at all.
Cedarville is the best Last Stop Before Playa. It has become a very burner-friendly town. The gas station at the corner that you'll see as you get to the bottom of the pass and hit town is open late and the owner usually has a BBQ going. There's a NAPA store so you can get whatever you need to solve any vehicle issues. There's a great restaurant in the middle of town ("town" is only a couple blocks of main street, you'll find it).
I never bother with trying to stop in Gerlach, it's tiny and overcrowded with other burners. Cedarville is much nicer and it's close enough to be a good jumping-off point.
Making a two-day trip means you'll be hitting all these places while they are open, and you'll have plenty of time to do your last-minute shopping.
"Whaoomph! Whaomph! Burbbleburbblepattpattpattpatt... WHAAAAAaaoooaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa........!!!"
Top fuel dragster, by Elliot Naess