Biking fom Tucson to Albuquerque

Visiting my cousins in Tucson and Albuquerque, AZ and NM I like to go from TUS to ABQ by bike.
Some questions:
1. What about buying one in Tucson. Taking my own costs 3 (flights) x $ 90 fot transport and a chance for damage or late arrival.
Cannondale is famous here!?
2. Is it easy to take the bike in Greyhound and Amtrak without booking in advance (for being flexible because of weather, distance or physical condition and flight dates)
3. I plan April and like to visit Tcson and around, Grand Canyon and Chaco and of course ABQ.
Then back to Phoenix (Sky Harbur Airport) by Greyhound?
4. I don't take much luggage so need lodging underway. Any advice for motels or whatever? (I expect that's pretty cold in the nights to camp without taking many clothes?!)

Any other advice?
I would be grateful!!!!

I would think buying a bike in Tucson would be no problem. Maybe try craigslist.com or the classifieds to get a bargain used bike. I hope you are in good physical condition, because it is a great distance between all of those places you mention. Grand Canyon being totally out of the way and not at all between Tucson and Albuquerque. I actually don't know anything about Greyhound and difficulty with bikes on it. Tucson is a great town. Sonora Desert Museum is cool.

Thanks jbur,
physical condition is okay but anyhow I need some parts by transport, let's say to Flagstaff to have time to look around.
That's why it's important to know about buses. Amtrak back from ABQ to Flagstaff is no problem.
But nicer seems to me the bustour ABQ - Tucson via Las Cruses so that I ride the clockway round. Mountains and desert. And about Tucson you confirm my cousins (subjective?) meaning.

Arie

Keep in mind that it gets really cold when the sun goes down, especially in April. Prepare for weather extremes. I'd err on the side of caution, no matter what you do, because it is desolate with a capital no-one-for-miles out there. There are stretches where you could easily go nearly 100 miles without any kind of services. As an example, my parents live in Colorado, and there is a sign not far to the south of where they live that says, "Next services 74 miles." In other words, get gas or food/drink now.

I've never had problems taking large items on Amtrak. A bicycle shouldn't be too much of a problem, especially once you take the front tire off. Greyhound might be a bit harder, simply because storage is more limited.

I've always had the best luck with inexpensive accommodation just by going to an online discount service like Priceline.com. I don't know if you can access that from the Netherlands, but that's one route. If not, Super 8 has an easy phone number to remember, they're nearly everywhere, and they're usually pretty cheap, mostly reliably comfortable rooms.