passenger ferries/speedboats run daily every half hour from 7am till 6pm, car ferries run daily 4 times a day
just go to Telaga Punggur ferry terminal on Batam's east coast, and pick your destination:
a) Tanjung Uban, about 15 minutes by speedboat, 1 hour by car ferry
b) Tanjung Pinang, 60 minutes by passenger ferry
Follow up question to the OPs and noting the answer given so far:
1. Is it just a simple case of arriving at BTH and getting a taxi for the 15Km journey around to Telaga Punggur ferry terminal on Batam? Is there a regular shuttle that does that trip? Indicative cost?
2. Do the ferries / boats have any sort of schedule for running from Telaga Punggur to BBT? If not, about how often do they depart? And when would the last one depart Telaga Punggur?
3. Is it easier to simply fly into Tanjungpinang airport (TNJ) and take the ~90 min land transfer to the resorts area? This is not my preferred option as there are many more flights and preferable timings to go into BTH.
There does appear to be only a little info out in internetland and much of that appears out of date, so hopefully someone has an up to date response.