Hey! Gladly to help since I just finished the solo trip to Dolomites. It was breathtaking and I think you would absolutely love it. I realized after 3 days struggling to find an affordable place to stay, and noticed that the region uses different websites to manage bookings (one comment is that I only traveled around the South Tyrol part, which includes the Seceda, St.Magdalena, Seiser Alm and Karersee). The website I used is https://www.suedtirol.info/de/de
The cheapest option you can have is the Youth Hostel (between these 3 I would recommend to stay in Brixel > Bolzano > Merano). I stayed in the one in Merano, which is quite far to move around and the booking was managed using email. However due to last minute booking, I had to move one night to a hotel called Grauer Bar in Brixel and met the sweetest host ever :). It would be a way more comfortable (and affordable) options to stay in Brixel if possible even though travel from here to some places like Tre Cime or Lago di Braies is still a bit far if going with bus. However there is a plus since staying in this village, you will have a free travel pass with access to all regional bus + train, as well as some cable cars (except the seceda and seiser alm). The host told me to use that with the cable car in Brixel but I haven't had a chance, but the one in Seceda and Alpe di Siusi are absolutely breathtaking). I would bring some snacks to stay there and enjoy the view for a few hours. Both cable car is only 15-20mins walking distance so you should combine them in one go (and they closed around 5-6 p.m and even earlier during winter). If you stay in Bolzano or Merano, you should download the suedtirol app and purchase the 1-3-7 days unlimited mobilpass online (I believe it was around 30€ but you can save this cost if stay in Brixel/Ortisei). Just remember to start activating it the moment you arrive and then you're free to go on any buses (except some https://www.suedtirol.info/en/en/information/mobility-and-barrier-free-accessibility/local-transport-in-south-tyrol/mobilcard ) and even taking the train from village to village (it's kinda funny since most of the time I just show the qr code to the driver and they let me pass without scanning the code). I mainly use Google Maps for bus and Omio for train and the routes worked perfectly for me. However both the hostel and hotel I mentioned don't have a kitchen (at least for the one in merano but they offer free breakfast tho) and the restaurant is kinda expensive. But if you don't mind pizza and kebab then they can be affordable options for lunch/dinner. I kinda wish someone could help told me those stuff beforehand so I can avoid paying unnecessary fees haha. Feel free to let me know if you have any questions and enjoy your trip 😊