Here's all you need to know about the tunnels. With your 30' it shouldn't be any issue. After you go through the tunnels and before you being going down, downshift so you won't have to use your brakes constantly. You'll be down before you know it! :)
With your 30' Motorhome you won't need a permit and it will be free to drive. The permit/fee is for larger RVs.
https://www.nps.gov/zion/planyourvisit/the-zion-mount-carmel-tunnel.htmIf you want to avoid the tunnels you can take one of two other routes to Springdale.
1) From Bryce take 89 north to Hwy 20 west to I-15 south to Hwy 9 east to Springdale
2) From Bryce take 89 south just beyond Kanab, UT to Fredonia, AZ. Then take 389 west which becomes 59 in Utah and take it to Hwy 9 at Hurricane. Then east on Hwy 9 to Springdale.