My well-informed guess is that it is very unlikely that whole bacteria can enter the blood from the gut in SIBO. If that happened it would probably lead to septicemia (bacteria growing in the blood), which is a very serious acute life-threatening illness, needing urgent treatment - I can't find anything about septicemia in the context of SIBO in PubMed.

You are right about lipopolysaccharides - they could well enter the blood because of the increased intestinal permeability in SIBO - their endotoxin action would be a serious concern if that happens.

As far as I can see Rifaximin is front-line antibiotic treatment for SIBO - I hope that it works for you.