The Bukit Peninsula is connected to Kuta through Jimbaran by the busy Jalan Bypass Nusa Dua and this is the only route in. Take this main road south to the junction with Jalan Uluwatu II the famous McDonald's junction, turn west towards Jimbaran Bay, continue about 2 km and at the four road junction make a sharp left up the hill signposted for Uluwatu. Continue on this road into the heart of the peninsula.
A taxi from Kuta to Uluwatu for example takes 30 to 40 minutes on winding roads and will cost about Rp 120,000 one-way. If you are just visiting for the day, consider asking the driver to wait trip as it can be difficult to find transport back. Figure on paying the taxi driver Rp 20,000/hour to wait. Joining a tour can be a cheaper way of getting to Uluwatu and this destination is very widely offered by tour operators all over the island.