Let's break this down.
Fact One: Both have extremely high reaction speeds, but Bug Eaten's doesn't matter since it's impossible to dodge Heaven's Door.
Fact Two: Rohan's range is unknown, as he's fired and hit people an unknown distance away. However, in fights such as HA Dio vs Rohan, it was not a question that Rohan could get to him even when the range was 200 meters. This is only 100 meters.
Fact Three: Rohan will go first. His Stand only requires somatic components of pointing, if that at all. He'd be able to do it before Ratt can aim and fire.
Fact Four: Bug-Eaten doesn't actually fire that quickly! Not only did Josuke respond fast enough to think about his decisions, grab a pan, and then block the hit, but Bug-Eaten also needs time to aim and prepare to fire. He's not capable of going semi-auto and mowing Rohan down.
With that in mind, how does Rohan lose more than he wins?
I never claimed Rohan was multiversal, but multiversal is much larger than 100 meters. Strawman.
There have been times he's used it at farther but unknown ranges, as well.
Rohan, as per SBA, knows he's fighting and can be assumed he knows where the opponent starts. But OP can clarify this.
Rohan has acted extremely quickly under pressure: He responded to Koichi having his soul and body taken completely calmly, and that's far more tense than a rat shooting you.
Jotaro was mostly acting as a target while Josuke practiced his aim. Plus, Jotaro was out of practice.
Also, yes, Heaven's Door can affect Bug-Eaten. Why in the world wouldn't it?
Tl:dr: Range is unknown but fights with larger starting distances have had Rohan win, so it's unlikely that his range is 10 feet. It's at least considerable enough to hit Ratt from 100 meters, or enough to get close. Rohan's acted very calm and very swiftly under tense situations, such as Koichi getting ripped apart in the alleyway. All arguments for Bug Eaten hinge on Rohan having a pitiful range.