Hello & welcome
I can travel by bicycle and experience good art.
I'd imagine good art is in the eye of the beholder, no?
It's not clear where you are, where you might like to go, what kind of experience you have or if you want to do this on your own, in a group, as part of an organised tour, perhaps? Or indeed what kind of art.
I recall
@dimrub doing a musically inspired, organised tour (but I can't find it now).
I myself made something of a musical pilgrimage.
CrazyGuyOnABike will probably have some inspiration. It has a very useful search function.
If looking for an organised tour, Google is your friend.
If looking for a DIY type itinerary, arm yourself with a good route planner (I recommend
CycleTravel), pick where you want to go based on the art (check the opening times of the museums if that's your thing) and off you go.
My first cycling holiday was terrifying to contemplate but in reality was a gentle wander along the Danube from Passau to Vienna. I don't recall a lot of art along the way but Vienna in August was stunning with beautiful architecture, great street entertainment and lots of people relaxing and enjoying themselves.
If you've not had a cycling holiday before I heartily recommend it - but be careful - you never know where that bike will bring you