You may not need to get a cab, but it would save you a good chunk of time. Time that could be spent sleeping.
The latest you should be out at the bus stop is 6:30 am. And then you will need to wait and hope it is not too long before one comes along. And then if you get lucky the bus driver will drop you off right at the Contemporary. That is not a given. Otherwise you need to take a bus to the Magic Kingdom and either walk or monorail to the Contemporary resort.
With a cab you simply get in the cab, and go directly to the resort. No muss, no fuss, no worrying about if you just missed a bus and when will the next one be along, and then will they drop you at the Contemporary or won't they.
To me using the buses for early morning ADRs is too much hassle and too much stress. Much simpler to get in a cab and go.