When you ran out, you probably sucked up dirt, rust, and other nasty stuff from the bottom of the tank.
It could have choked off the screen on the pickup tube in the tank, but normally fresh gas will flush it loose.
The fuel filter definitely needs changed though. I'd bet if you take it off, and dump it out into a paper towel, all kinds of nasty stuff will come out.
That's why it bogs and backfires,the carb opens up but it can't get enough gas.
It probably idles fine, and runs fine up until about 1/2 throttle if you ease into the throttle????