The encounter rate in most outdoor locations (grass, Route 111's sand, etc., but not surfing or caves) is 11% per step while walking or running (1/9.09), or 8.889% per step while riding a bike (1/11.25).
Leading your party with a Pokemon that has Illuminate doubles your encounter rate. Using a White Flute increases the encounter rate by 1.5x, but I could not find any information about when or how the White Flute wears off, or how often you would need to refresh it, so I'm excluding it from my calculations.
After timing myself in Emerald both running and on the acro bike, the time averaged out to about 0.125 seconds per step while running, and 0.1 seconds per step while on the acro bike. I did not test the mach bike because its speed varies, making it too inconsistent.
I also timed myself running away from wild Pokemon, and found that the fastest you can run away takes about 12.5 seconds with battle animations turned off (to skip the Pokemon cry animations).
Let's also assume that you're not 100% efficient, and tack a 1.3x multiplier onto the end, to account for any miscellaneous lost time.
Source for encounter rates
Running: ( 0.125 seconds per step * 9.09 steps + 12.5 seconds to run away ) * 8192 encounters * 1.3 = 145,221 seconds, or 40 hours, 20 minutes, and 21 seconds
With Illuminate: ( 0.125 seconds per step * 4.545 steps + 12.5 seconds to run away ) * 8192 encounters * 1.3 = 139,170 seconds, or 38 hours, 39 minutes, and 30 seconds
Acro Bike: ( 0.1 seconds per step * 11.25 steps + 12.5 seconds to run away ) * 8192 encounters * 1.3 = 145,101 seconds, or 40 hours, 18 minutes, and 21 seconds
With Illuminate: ( 0.1 seconds per step * 5.625 steps + 12.5 seconds to run away ) * 8192 encounters * 1.3 = 139,110 seconds, or 38 hours, 40 minutes, and 30 seconds
