Learn English – “Till the morning” or “till morning”

@RegDwight is correct in every particular. Till is indeed older and the two can be used pretty much interchangeably.

There is really only one usage I can think of where you would not use till: in setting up a negative conditional.

Until my landlord fixes the plumbing, I am not going to pay the rent.

I am not going to pay the rent until my landlord fixes the plumbing.

Here it would sound strange to use till, and I'm not really sure why. Perhaps it is the negative.

One more thing. Sometimes you will see people spell till as a contraction of until: that is, as 'til. This is simply wrong, and not seen outside of old poetry and modern greeting cards aiming for a "poetic" tone. Anywhere you see 'til being used, till would be the correct word.

Both are fluent and natural, but they have different meanings.

I am... means that not only have you made the decision to go to bed imminently or get off the bus, but you are actively doing that — finishing off a drink or TV programme, or moving towards the bus doors.

I will be... means that you have made the decision to go to bed or get off the bus soon but you haven't actually done anything about it yet.

The import of each sentence is implicit in the tense used. I am is present tense and you are actually in the process of doing the action; I will be is future tense and although you know you will be doing something, you haven't started yet.