Dolomites Should we stay in Bolzano or Ortisei?

Ortisei. The capital of the Val Gardena.
Bolzano is not even on the Dolomites. It's at the bottom of the Adige valley that in summer reaches temperatures of over 30-35 Centigrade.
Check Villa Emilia in Ortisei, which is not expensive. However there are lots of accommodations in town. Do some searches online. Try to find a place that is not out of town, since you are relying on buses.

Ortesei for sure! Or the next town up, Santa Cristina. We stayed there a couple years ago, at Hotel,Villa Martha. Not inexpensive,,but the food was amazing ( we did half-board) and the welcome was warm and genuine. We had great views of Sassolongho ( spelling?) from our balcony. There was a great hike right from the hotel. For another, we rented bikes and rode to Ortesei and took the cablecar up to Alpe di Siusu to ride bikes. Another good one would be the cablecar up to Alpe di Siusi from Santa Cristina ( it wasn't running when we were there).

You can get all around by bus.

Thank you for your replies.

I've only done street riding about 25 miles, hills, but not mountains. Would bike riding be possible for my
level?

The bike ride we did on Alpe I'd Siusi was on designated bike trails, which were gravel (unpaved) roads. We rented mountain bikes but not the full suspension kind. They had wider tires that did fine on the dirt and gravel. There were some hills but if it was too steep we just got off and pushed the bikes. Most of it was rolling terrain, very pretty. The main uphill part was getting back to the cablecars.

I just read in Rick Steves book that Ortisei and the towns around there seem pretty shut down in May and half of June. Also all the hotels seemed to be offering only seven night stays and we wanted to srtay about five nights. The book says that the lifts are not working and the trails are still covered in snow in May.
Does anyone know anything about this?

Here is the summer schedule for 2013. It is still the height of ski season, so the summer 2014 schedule won't be out for a while.
http://www.valgardena.it/fileadmin/template/files/pdf/Lifts_Summer2013.pdf
As you can see, a lot of the lifts will not be operating until mid June and some until July, but the Ortisei-Alpe di Siusi cable car opened May 19.

Thank you. It looks like if we go to the Dolomites in Mid May we will be going to a quiet place and enjoying the views, will miss the trams and most of the hikes and bike rides due to the snow and mud. It still seems like a worthwhile way to spend 3-4 days.
I think that there are 5-6 places open year round at that time.