Instead of taking a tourist bus where you can hit all mainstream attractions ranked on tourist sites, you can be individual, active and green all at once.
There are several ways to discover the center of Budapest center and what I suggest you now is a combination of public transport, walking and riding a scooter!
Budapest offers car sharing (MOL Limo), e-scooters (Blinkee) and bikes (Donkey Republic). I personally use car sharing and bikes often but as a tourist Lime Rollers will do the service for you. The city center is packed with the shared vehicles, scooters and bikes so you will easily find one. Riding alongside the River Danube, in the shopping and museum district is safe but always be careful and follow the traffic rules.
Scooters are handy, just download the app and read the QR of any scooter. You can pick it up and leave it anywhere you like, so you do not need to bother with returning it to the dock. It will cost you less but will be fun!