Hi Cat. We started the TransAm Aug 1 from Florence, OR & motelled it all the way to Kansas (where my husband fell and broke his collarbone and sagged us in an RV the rest of the way).
So it can be done, but you have to plan VERY carefully unless you're capable of 100+ mile days. You can use my journal as a template, our days averaged 43 miles and the longest one was 80 miles in Kansas. (We combined two 40 mile days because we wanted to get ahead of a storm and keep motel reservations that we already had). Reserving motels in key spots is your biggest challenge, start by figuring out what date you'll be in Grant Village, Yellowstone, and get those reservations online first.
Reserve a few days, then you can cancel 48 hours in adance with no penalty once you've narrowed it
down to the one night you need. Average motel cost was $85 for the first half into Pueblo, CO. I
haven't done the figures past there yet, but motels got cheaper in the midwest.
Other spots on my route that are key for reservations are:
McKenzie Bridge, OR (Caddisfly Resort was booked in Feb, there are other cabins but $$$)
Jeffrey City, WY (Byron has just the one trailer that he *rents* out for donations)
Consider splitting the day from White Bird to Lowell into two days: White Bird to Grangeville, Grangeville to Lowell. The *hill* out of White Bird is a bit€# and even a very strong cyclist we rode with (wisely) stopped in Grangeville.
A lot of western towns have only one lodging but everybody is cool about reservations when you tell them you're bicycling. They're not gonna charge you if something happens and you don't make it as long as you call. My advice would be to make reservations for the western half months in advance like I did. I used the ACA maps, which show where the mountains are, to decide where to stay. A 30 mile day up a mountain pass is more strenuous than 60 miles on the flats, so pay attention to that! I was very careful not to end a long day with a mountain pass either. Better to start the following day with that mountain pass.
Past Pueblo, lodging isn't hard to get. Do call ahead and reserve a day or two in advance so you don't get skunked, but it doesn't have to be months / weeks in advance like some of the western towns.
The western half of the TransAm is safe for a woman. People are used to seeing cyclists. There will be plenty of other cyclists out there and you may be able to cut expenses by sharing motel rooms. There aren't many hostels along the way, you may hit one every 10 days or so. Sometimes you need sleeping bags for hostels so you'd have to decide if you want to carry one just to use a few times.
The standard American motel room is two beds and it's often the same cost for a room for one vs. a room for two people. The first half, I was with my husband, so one bed. Oftentimes, however, the motels gave us a room with two beds because there was more room for the bikes and the cost was the same. The second half, we added my sister, so three people and always rooms with two beds. Some rooms were ~ $10 more for the three of us, but many were the same cost as with two people.
All the prices and contact info for the lodgings is in my journal:http://bicyclelife.topicwise.com/doc/?o=1&doc_id=9261&v=3Df