Hi Debbie
I'd echo what Mick said - I'm a total tea-pot and I've never yet found a 'proper' cup of tea in the US! I'm sorry to say it but I don't think Americans really 'get' tea. Even if they offer it, it usually comes with cream rather than milk.
As a suggestion, the rooms usually have a kettle. I gave up taking tea bags because I don't drink it black and they don't offer UHT cartons like those you get in the UK or Europe. Instead, I always pack a supply of Instant Hot Chocolate sachets (Galaxy, Maltesers, Options etc) which just need hot water. Alternatively, you may prefer to take herbal tea bags so, again, you wouldn't have to worry about milk.
Either way, and as I'm sure your TM will tell you, this is a very busy and dehydrating tour so be sure you always have a bottle of water in your bag. Our driver very kindly had a cool box in the back of the bus and kept it stocked so that, if we had forgotten to pick up a bottle at the previous stop, we could always give him a dollar for emergency supplies. Believe me - once you hit the Nevada desert, you'll really need it.
All the best
Mandy