Good question. It helps to illustrate how scientists, engineers, and mathematicians approach real-world questions.

As you know, the potential riders are going to be breathing out a certain amount of CO₂ just by being alive. Let’s call that their base CO₂.

According to this site:
release-of-carbon-dioxide-by-individual- humans
humans burn about 700-900 g of carbon per day. This is a rough estimate because size, activity level, and such would all influence the number.

So let’s say about 33 g of CO₂ an hour (800 g/day divided by 24 hours/day). If I am sitting still, I burn about 1 calorie per minute. When I walk or ride my bike, I burn about 4. I happen to know this from an exercise device I wear. So let’s say that riding my bike, I’m producing 133 g CO₂ (33 g/hour at rest X 4-fold increase in energy use). I would go about 15 miles in an hour at my usual pace. But remember that I’ll be breathing even if I’m not biking, so the additional CO₂ that biking would produce is only 100 g CO₂ for 15 miles of travel (33 g/hour at rest X 3-fold addition in energy use). For one person to bike 15 miles, 100 g of additional CO₂ are produced.

I had no idea how much CO₂ a bus might give off, but according to this site:
comparative energy
a typical city bus gives off about 300 g of CO₂ per passenger mile. That’s not per mile the bus drives, it’s the CO₂/miles divided by the estimated number of passengers on the bus (I think their assumption was about 25 people). To carry one person 15 miles on a bus would be 4500 g CO₂.

As you can see, biking will result in much lower CO₂ output.

This should give you some idea about how scientists use models. We make predictions based on logical calculations and estimates taken from real life. Deciding which values are reasonable and which variables to include can be a challenge.

Let’s say that I tell you that the CO₂ exhaled by the biker will also be balanced by the CO₂ taken in by the biker as food. If I burn a molecule of sugar, I give off 6 molecules of CO₂. When a plant makes a molecule of sugar, it has to take in 6 CO₂ molecules during photosynthesis. The diesel fuel burned by the bus was from oil produced from things that died millions of years ago. This is all true, but it leaves out some important information.

A lot of energy is used to produce the food that modern humans eat, so to be fair, you would have to consider the fuel burned by farming, food factories, food transportation and preparation, plus the costs of disposing of wastes like packaging. BUT you would also have to consider that I could get enough energy for that hour of bike riding from 320 total calories, or 240 added calories (subtracting the 60 I would spend from sitting down for an hour). That’s only about 1 granola bar. (If you consider that I will burn some energy digesting the granola bar, maybe I can add a bite of fruit, but let’s keep it simple.) How much CO2 was produced to get me that granola bar? See what you can figure out.

If these questions interest you, you might consider studying environmental science or mathematical modeling.