If a person uses public transport, how much carbon is added to the footprint?
I'm no expert on such subjects, but did Google and immediately this Guardian article offering a dataset apparently attributed to Camden Council/travelfootprint.org/Clear Zone Partnership.  There are a lot of different values, but (if I understand the columns labels correctly), a rough breakdown of the footprints would be ranges of:

Bus: 20-90 g CO$_2$/km
Train, Diesel/Diesel-Electric: 30-150 g CO$_2$/km
Train, Electric [Long-Distance or Subway]: 10-70 g CO$_2$/km
Flight: 190-460 g CO$_2$/km  

Walking: 5-25 g CO$_2$/km
Biking: 7-18 g CO$_2$/km  

Basic car, Diesel: 40-180 g CO$_2$/km
Basic car, Gasoline: 40-200 g CO$_2$/km
Basic car, Liquefied Petroleum: 30-180 g CO$_2$/km
Basic car, Natural Gas: 30-150 g CO$_2$/km
Basic car, Gasoline Hybrid: 30-150 g CO$_2$/km
Basic car, Electric: 7-110 g CO$_2$/km
Motorcycle: 20-190 g CO$_2$/km
Scooter, Electric: 4-30 g CO$_2$/km  

[See the report for other automobiles, including family cars, SUV, and minis]

(The best end of the range is the more efficient models run at peak capacity in best conditions [rural roads/medium distance short-haul flights]
The worst end of the range is less-efficient models at quite low capacity in less-efficient conditions [urban roads/very short or long-haul flights]
[Rail appears fairly similar in all usage circumstances, thus only depending on model/network setup, at least in this UK data])

This data attempts to take into account secondary sources (such as power plants for electric vehicles or needs of the agriculture which is used for the energy to walk/bike).  As you can see there's a wide range depending on how most transport is used.  You're best suited diving further into the table to find the most applicable use case for you.

My list only shows CO$_2$... the database also includes NO$_2$ and some others pollutants (if you can break down the abbreviations!) which can be very important too.

And this is UK-specific.  So the equipment models used, network efficiency, and even climatological conditions will vary for other locations. 

The date on the article also suggests its almost a decade old.  So we have likely seen some additional improvements in some formats (though it seems unlikely that they are giant leaps in most cases).

Hopefully someone will come along with more recent and wide-ranging data, but this seems like a good start at some rough estimates.