Solo is fine David. The first few miles up the trail will seem very similar to what you've done at Baldy. You can also take your time to explore and kick around without having to shepherd other folks.
Yes, you'll get on a first name basis with the rangers at Bishop who man the phones, but they're used to it. Between my wife and I, I bet we called 70-80 times in July before we finally nabbed two cancellations - and that was two days out.