It's been 10 years since I went, but I'm pretty sure it's still walk-only. They've added a couple of courses since (there were 4 then: Bandon Dunes/Trails, Pacific Dunes, and Old McDonald), but I don't think there are carts anywhere at the club.
Thankfully the caddies know the course (and rough) so well, you almost never lose a ball. Even when I'd hit a kite up into that wind (it's very gusty along the pacific as you can imagine), I hardly lost any balls because those guys are like bird dogs and would go right to it. So at least you don't waste a lot of steps searching... but you still walk a LOT.
Great trip, highly recommend any golfers go at least once.