There are, at least, two reactions taking place and causing the brown colour of your bread. One is the oxidation of monophenols by an enzyme called PPO and the other is Maillard reaction, which is the same reaction that makes your steak looks deliciously brown.
Reaction 1. Oxidation of monophenols.
Bananas have a lot of polyphenol oxidase (also known as phenolase or PPO), an enzyme that catalyzes the oxidation of polyphenols naturally present in the banana fruit. The product is a colored ortho-quinone, which is brown or dark reddish. When you smash bananas to make a banana bread you end up releasing a lot of PPO which will catalyze the polymerization of the phenols and, therefore, make your bred looks darker then others. Below is a representation of the oxidation of monophenols into the colored ortho-quinone.
Reaction 2. Maillard reaction
The Maillard reaction is one of the most important reactions in food chemistry. Its products can add sensory features to many preparations, from steaks to coffee. Basically, sugars from the ingredients react with an aminoacid's amine group to form a glycosylamine. This compound is then isomerized to a ketosamine, which breaks into smaller substances. These substances are the Maillard products, and one class is called Melanoidins, responsible for the dark spots in your bread.
The reason why it is formed when you add sodium bicarbonate to the mixture is because alkaline media speed up the fragmentation of the ketosamine, yielding more Maillard products. 2
I have included an infographic from CompoundChem with other information and the Maillard reaction in chemical notation.
2Owusu-Apenten R., Introduction to Food Chemistry, CRC Press, 2004