Hi, Peter! "Steph" here. ( The system here picked my full legal name off of my credit card. I have to change my screen name. My Momma didn't even call me that....even if she was mad at me!)
Griff does cover the"thump bass" done on the 6th and 5th strings starting in Lesson 15 of ABGU. This is why he has us study the "Little Chords" earlier in Lesson 10. They are all I, IV and V 7th chords that are solely on the first 4 strings. At this point you can using your thumb to create the bass part or a pick and use fingers for the other notes. The first full length blues piece in Lesson 10, which Griff has you prepping for in the previous few lessons, he plays in "hybrid picking" on the DVD: holding a pick between his thumb and index finger, and using other fingers for notes on the first 3 strings. Some of his other pieces of music are all out fingerstyle, using the thump bass with his thumb. He stresses, in Lesson 2, trying to not get addicted to one method of playing and stresses trying to remain fluid.
I am currently sticking devotedly to Griff's ABGU. I love it and am literally rolling around in it with the same abandon that a farm dog rolls around in manure. I am sticking to it like glue. I started that course, and All Access Pass, on August 1, 2020 after starting BBG and some of his more elementary books as review. I am working on "Down To The Station" in Lesson 14 and truly enjoying it. I have come so far in the past year! I started studying his material in the 3rd week of March 2020 when Covid 19 shut the world down. (I think his courses and AAP saved my sanity with what has been going on.)
There is a book that is highly regarded, written by Joseph Alexander, titled "Fingerstyle Blues Guitar". I have it and it is available at Amazon.com.
He devotes the first 11 pages of it to creating "thumb independence" from the other fingers. He gives exercises to ingrain appropriate finger choice.
Personally, I would stick with Griff for the lion's share of your study, and just examine the first 11 pages in that book. It might be good to finish Griffs course and go to Alexander's book for material more focused on fingerstyle playing. I also can see myself studying BGU, although I will probably be playing solo mostly. I'm sure some of the material will be relevant.