Honestly, pretty fast. You could look at cases of bowel rupture, where a large amount of bacteria quickly gains access to the bloodstream, causing sepsis and rapid death without immediate intervention. Can go from infection to death in half a day.
If we're just asking for a severe response instead of death, it just depends on how severe it needs to be. The bacteria is throughout your body within minutes, flowing at the speed your blood circulates, and almost immediately triggering a massive immune response. This immune response leads to shock, which is what kills you.