Is there a bus from Tsim Sha Tsui to Shenzhen airport?

The transportation is convenient. You are suggested to take the direct long-distance bus at East Tsim Sha Tsui Station. The schedules are from 11:50 to 18:20 at intervals of 30 mins. It costs 130 HKD per person.
Well, the official website doesn't have English version. You can dial (+86) 2230 3030 to consult more information and book the tickets in advance.

Thanks Quella.

Do you mean they don't start earlier than 11.50am?

How long does it take from TST to Shenzhen airport using this bus?

Yes, the earliest schedule from East TST is at 11:50.
If you wanna take ealier bus, you can go to Jordan Station (also nearby TST). The buses depart from 07:00 to 20:00 at intervals of 30 mins. And the ticket fare is the same.
Generally speaking, the duration is 90 to 105 mins (excluded the clearance time). It's suggested to take the bus about 3.5 hours in advance.