The Care Quality Commission (CQC) visited Southmead Hospital last month after failings were identified during an inspection last December.
These included A&E patients waiting on trolleys for more than 12 hours until a bed became available.
The chief inspector of hospitals said "real progress" had been made. The hospital said it welcomed the report.
During the inspection in December, inspectors found "significant issues" with the flow of patients through the hospital and that the four-hour target for patients attending A&E to be admitted, discharged or transferred was not being met.
The CQC returned in May and despite "some improvement" found A&E patients were still "waiting too long for pain relief or treatment".
Now, chief inspector Prof Sir Mike Richards said the four-hour target was being met "most of the time" and additional staff were available to "cope in peak times".
Andrea Young, chief executive of North Bristol NHS Trust, said it welcomed the latest report which "positively reflects the many changes and improvements".
"Although this report has highlighted the positive work that has been undertaken, we are far from complacent," she said.
"Our focus is now on maintaining these standards throughout the winter period."
Significant improvements have been made in emergency services at Bristol's newest hospital, inspectors have said.