The easiest way to get to Nusa Lembogan is by boat. You will easily find boats in Sanur, Bali. The journey takes approximately 35 mins. From there you can easily reach Mangrove Forest by rental bike or motorbike.

Bali Swing
The best option is to rent a scooter for 5-10$ per day. It takes 20 minutes to drive from Ubud
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I suggest renting a paddleboard, the experience is better that way