Yes, Bilbao is great. There are foreign tourists around the Guggenheim, but that's about it.
I think the bus route will take you through Leon, Burgos and Vitoria-Gasteiz, all of which I enjoyed during a 2016 trip.
Leon has a large, attractive historic district that is now full of restaurants and bars. That's not my sort of scene, but it seemed very festive (in the summer). I assume most of the folks I saw out and about were Spaniards. There are some points of tourist interest in the city, including the cathedral.
The historic center of Burgos was full of pilgrims during my visit. It, too, is very attractive. It is notorious for being windy, though, which might not be ideal in April.
Vitoria-Gasteiz is the capital of the interior Basque province of Alava. It has a large historic district up on a hill, charmingly called the "medieval almond" because of its shape. It seemed quieter than Leon and Burgos, though it could just have been my timing. It was raining on the day of my visit. V-G has a couple of small art museums and a playing-card museum.
Any of those places would be worthwhile stops. One smaller possibility is the very atmospheric hilltown of Laguardia, which is on the bus line between Vitoria-Gasteiz and Logrono. Unless there's something strange about bus schedules in spring vs. summer, I think you could do a day-trip there from V-G, though quite possibly not on a Sunday. I observed some wine bars in LaGuardia; it may get some wine tourism since its near the LaRioja vineyards. I happened to hit the town on the day of a fiesta, so I couldn't tell how touristy it normally is. I think this is more a place to go for just wandering around than for ticking off a long list of sights, but I recall there's an important feature in an old church in the town. I didn't get to see it because (according to my guidebook) the key is held by the tourist office, and the T.O. was closed because of the fiesta.
The town of Astorga, west of Leon, has an Episcopal Palace designed by Gaudi and a few other sights worth a look. I traveled there by bus from Leon and am not sure whether through buses heading from Santiago de Compostela to Leon would stop there. It's small enough that you might prefer it as a part-day side-trip from Leon.