We do a lot of theory collectively working on paper on melodies to identify notes and their relationship with the harmony. Some things puzzle me, for example: a D is considered fine on C9 while a C is foreign, because it would be correct in a bass line but not in the solo.
This makes no sense to me at all. I'd really love to hear the instructor's reasoning for not wanting a soloist to play the root of a chord.
If you want to learn walking bass, you'd probably be better off with a private bass teacher who was experienced at walking and willing to teach it to you. I don't think there are many classes out there in walking bass.
Theory classes with lots of written assignments can reinforce your knowledge of note names, chord names, scale notes, etc. Of course, you should be able to play and hear anything that you are writing down. That should be an important part of your homework.
This class you are taking is for electric bass? I'm also puzzled as to why they are starting with soloing concepts. I'm curious as to what the double bass class covers.
Talk to a faculty member at your school and tell them what it is that you want to learn. Ask them if that is part of the curriculum.