Ronster, I understand where you're coming from about "spoon-fed vs missing detail" and I admire that you're trying hard to pay attention to all details, but I do believe this sequence where Boba is following Han explains itself well enough as is.

All we need to know is:

Boba somehow knew how Han was hiding and which Star Destroyer it was on (in my experience there's no such thing as luck).

His ship was ejected with the garbage, "offline" and unnoticed/undetected by Han.

After Boba saw the MF leave the garbage, he eventually turned his ship "online", left the garbage also, and followed Han out in deep space for however long, still undetected (the increased distance by Ady helps as a probable cause why Boba was undetected - he was too far out of range)

We find out later that somewhere along the way, Boba learned where Han and co. were heading and then notified the Empire.

It's unknown if Boba got to Bespin before, after, or the same time as the MF (we don't need to know which), but we do find out that the Empire got there before the MF did...

Other than what the footage already shows us for this part of the movie, we really don't need to know any more details about what happened or how it happened.