Typically the energy cycle your body uses looks like this if you're not resting while chasing the bike...
ATP for first 10-20 seconds(this is the fastest you'll go, but it only goes for 10 to 20 seconds).
Lactic-20 seconds to 70 seconds, sometimes more(moderately fast)
Aerobic 90 seconds onward(very slow, think jogging speed).
So over a couple minutes you can see how your speed will naturally decrease into a steady pace. You could train each energy system. You can train the capacity(how long you can go in each energy system), or the intensity(how fast you can go).
Given that this is more about endurance and keeping a high pace, you'll want to focus on the aerobic system. Time yourself jogging 5km or 6km.. then every other day try to beat your time record. Eventually you'll be running the entire time. This will improve your intensity. To improve your endurance, you could either just jog for as long as you can, measure how far you go, and try to go farther and farther each time while keeping the same pace. This will improve your capacity. You could also do metabolic conditioning workouts, HIIT, or tabata which can teach you how to use more energy without resting.
If your legs are getting tired you can also do endurance training(15+ reps) for your lower body to keep up with the endurance. You can look up workouts but either increase reps each week or increase weight.
If the bike keeps the same pace then you have no worries even if the distsnce increases. Unfortunately the best way to train is to do exactly what you're already doing but without the bike, and by the time you increase your stamina, the bike might have outpaced you