In general, Bali is considered a safe destination, since very few visitors come across any real problems.
Bali has been the scene of Islamic terrorist attacks targeting nightclubs and restaurants popular among foreign visitors in 2002 and other less notorious attacks averaging one/year over the last two decades, so remain vigilant and take special care since terrorist acts cannot be predicted.
When it comes to beaches, if there is a red flag planted in the sand, do not swim there, since the currents can be extremely strong.
To protect your money, use only authorized money changers, and when withdrawing money from ATM use the ones that are inside the bank.