Yup, it's a straightforward I-IV-V Blues progression with a little twist in that it has a 'Quick Change' up to the IV in the verses.
Bar-by-bar, the overall structure is basically this:
Intro (Bars 1 - 12): I - I - I - I, IV - IV - I - I, V - IV - I - I
Verse (Bars 13 - 24, 25 - 36): I - IV - I - I, IV - IV - I - I, V - IV - I - I
Solo (Bars 37 - 48): I - I - I - I, IV - IV - I - I, V - IV - I - I
Verse (Bars 49 - 60, 61 - 72): I - IV - I - I, IV - IV - I - I, V - IV - x - x (The x's are for the 2 bar stops)
Arm yourself with your trusty Pentatonic Scale... The core riff is AA-GE-GC-AA which Jack Bruce then takes great delight in varying subtly. It just gets transposed with the changes.
Whilst it's possible to transcribe every little bend that JB makes, and also show how he's playing off Ginger Baker, I feel it's wiser not to since TAB can't show the timing information & using notation would just result in a confusing mess of notes & rests - but, hey!, that's Jack Bruce all over

His line in Strange Brew is textbook Bruce - take it away & the song's
nothing.
Start with the very basics - treat it as a strict, repetitive blues, then gradually muck about with the notes. Leave some out, put a few in etc. etc. It's a
very hard thing to emulate as JB's a one-off, but it's possible to get into that vibe - not a five-minute job though. It takes time to build a blues vocabulary & everybody's ends up slightly different.
Pete.