If you're within walking distance to the beach, shops, and restaurants from your accommodation, and you'll only be going further for the odd sightseeing day, then you only need a private car and driver on an ad-hoc basis for day tours.
However, if you'll be going further than walking distance for most days, I highly recommend hiring a private car and driver for the full length of your stay. Having a driver on call for most if not the whole day and evening will help make your Bali holiday friction-free because you remove the hassle of constantly getting taxis in Bali, which can be a real pain.
Whether you and your crew are looking to spend the day at a beach club, visiting the unique attractions like temples, rice terraces, the Bali swings, some of the amazing waterfalls or just spending the day shopping, hiring a car and driver can make a huge difference.