Snow would be unlikely in May but as you know, it could happen. Is Bryce your only stop? You will be in the midst of other wonderful national parks. Any of the roads to any of them would be just fine for your 27'. You'll see much bigger ones traveling them.
If coming straight down I-15 south take Hwy 20 to Hwy 89 south to Bryce or I-15 to I-70 east to 89 south.
I-15 to 28 to 24 to Torrey and you could work in Capitol Reef NP and then take Hwy 12 to Bryce - a gorgeous drive and our favorite.
Hwy 89 south from Spanish Fork is another option. You can't go wrong on any of the highways in that vicinity.
From Bryce you could also go to Zion easily and the North Rim of Grand Canyon near Kanab, UT open May 15, I believe. Check on it.
Have a good trip. They are beautiful parks. Keep in mind that each national park has an awesome web site giving road conditions, special alerts, camping, things to do, etc. Check them out. Here is Bryce's:
https://www.nps.gov/brca/index.htm