I've put an unboxed bike on amtrak thruway bus cargo holds many times. I've even u-locked the bike to a support beam inside the bus. They normally give me my own little section of the cargo hold.
Also, if you're at LA union station, you've got a good chance of finding a previously used bike box or two from bike tourists... Just ask the station attendant if there are any. When I've boxed up my bike in LA I've always gotten a free one.
Oh, and just in case you wanted to know, there's also a coast route you can use to get down south from up here. You get on the capital corridor to oakland, take a thruway bus to santa barbara, and then the pacific surfliner from Santa Barbara to LA. It's the way I normally go, because it leaves at night and I don't mind sleeping on the bus.