Is there direct bus from Dazu Rock Carvings to Emeishan?

No, there is no direct bus between these two places nowadays. Thus you are suggested to take a coach from Dazu Bus Station and get to Chengdu East Bus Station first. I remember that the bus schedules are 07:00, 08:50, 09:50, 11:40 and 14:00. It costs CNY 85 per person. The duration is 4-5 hours.
After arriving, take a taxi to Xinnanmen Bus Station. There are many direct coaches to Emeishan. The last schedule is 19:00. The ticket fare is CNY 41 per person. The trip takes 2-3 hours.