Is there public transportation (train/bus) from Wuhan to Yellow Mountain?

Yes, direct buses to the mountain are available. At Fujiapo Bus Station, two buses are scheduled at 09:30 and 16:00. It takes 8h and costs CNY198 per person.

To travel by train, transfer is needed. At Hankou Rail Station, take a high speed train to Hefei South in 2.5-3h. At the same station, transfer to another high speed train to Huangshan North in 100min. After that, take the direct shuttle bus to the scenic area in 40-50min.