Is it expensive to have private transport on Bali?

No. On Bali it is still not expensive to have private transport during your vacation. Of course you can make it as expensive as you want. If you require Putu to accompany you every day and work for you exclusively, this will cost more then booking a few trips and combining that with your own exploring.

Indication:
Putu's trips start from 25 euro (lookup the price for your currency at www.exchangerates.com). All trip-prices are including car-hire, fuel and Putu's time.

Entrance fees, meals and drinks are not included.

If you just want to hire Putu for a shoppingtrip to Kuta, or to drive you to Jimbaran for a moonlight-dinner, this will cost you the fuel-costs and Putu's time.
Putu will always discuss the price with you upfront, so that you know exactly what you'll get and there will be no surprises.