score:6
There are a few private shuttle services serving the Eastern Sierras listed here that might be able to get you to Mammoth Lakes from Reno. They may be pretty expensive. The Eastern Sierras are sparsely populated and there is not much in the way of public transportation.
Note that flying to RNO in many cases would require a connection at a hub anyway, and so you might be able to fly directly to Mammoth Lakes (MMH) with the same number of segments. Since it is a skiing destination, I would expect that Sunday flights to Mammoth Lakes would probably be cheap and have lots of empty seats anyway (so the ecological impact may be minor); most passengers would be leaving Mammoth Lakes on Sunday, not arriving.
If you insist on going overland, your best bet will probably be to rent a car and drive. I would advise against traveling from SFO as you will have to cross the Sierras and there is still the possibility of winter weather in early May.
Do not expect to be able to reach Mammoth Lakes easily from any of the Central Valley airports or train stations (Merced, Fresno, etc) as most of the minor highways over the Sierras are closed in winter and may not be reopened by early May. In particular, CA-120 through Yosemite (the shortest route) is rarely reopened until mid-to-late May and often later. You would have to travel north to US-50 or south to CA-58.