Mountain biking and road cycling in between Yachts and drum circles
I have visited Ibiza twice. Once on a mountain bike for a short backpacking trip (read more about that particular trip here) around the island and for a five day van trip on which I had a road bike with me. In this article I will report a bit on the quality of riding both on and off road you can find over there.

The road cycling is comparable to the eastern part of Mallorca. Very good undulating back roads with the occasional longish (aka five kilometer) climb. There are no major climbs and the longest seems to be the road from Cala de Sant Vicent towards Sant Joan. The other longer uphill is from Sant Antoni to Sant Josep. However the second one is on a big road more of a drag than a real climb.
There is very little traffic on the northern part of the island and the roads are smaller. If you only have a day or two of riding anyways I would recommend to keep to the north. On the southern side you definitely notice more traffic, especially closer towards the two centers of Eivissa (Ibiza town) and Sant Antoni.
In summary there are enough roads to explore for a few days but if you want to do a week long road cycling holiday I would still recommend sticking to Mallorca.

On a mountain bike there is maybe a bit more to do here. On the one hand most third level roads are gravel but well maintained. So a good idea might be (if you are more of a gravel or XC bike person) to combine the small paved roads with the available gravel. This also would open up the southern part of the island a bit more than on a pure road ride.
On the other hand there are plenty of rocky trails to explore all over the island. The trails seem to be less harsh than is typical for the mountains of Mallorca or the Cami de Cavall on Menorca but be prepared to fix a puncture or two. From my bikepacking trip I learned that you can ride all around and across the island without touching tarmac for extended periods.

So cycling on Ibiza? Is it worth it? Well yes. For a few days both on a road or mountain bike but my guess is that it will get old after some time just because the island is a bit too small. The best thing in my opinion would be to take or rent a gravel bike and have your cake and eat it two if you ever visit the place.