While this is a very common practice, or at least theory among anglers, the problem is trying to find any scientific basis for the action, to which I haven't really been able to find any. The most commonly suggested reason as to why this supposedly works is due to the citric acid component of soft drinks, but that theory has two problems associated with it;
Citric acid is actually an anticoagulant that prevents blood clotting, and
Cola drinks, when compared to most other similar beverages actually have a very low citric acid component to them. Most every other citrus type drink including orange juice, lemon juice/lemonade or pineapple juice have from 2X to as much as 7X's the citric acid. If that's the primary reason, why not recommend one of those other drinks instead?
Other reasons I've seen speculated relate to the coldness of the drink acting as a vasoconstrictor, but if that was the case why not just use or recommend ice-water. Another theory is that it's the carbonation in the drink (CO2), but again that doesn't make any sense as blood normally carries carbon dioxide, bicarbonate, and carbonic acid as part of normal kidney/waste fuunction and regulation, trying to eliminate it from tissue. Too much of any of these in the blood actually leads to a serious medical condition.
A more likely scenario going on when you pour your drink on the fish is probably a stress reaction to some form of shock, very possibly related to the pH levels of the cola. Most common soft drinks we carry around with us have a range of pH values between 2.4 and 3.7. Mountain Dew and 7-Up both run around 3.2, while Coke, Cherry Coke and Pepsi are down around 2.5. It is very possible that the acid is either triggering a response due to the pH shock, as literature suggests that a common fish reaction to such a sudden change in pH is often excess mucosal production of the gills to try and protect itself, or even a chemical burn or weak cauterization of the delicate gill tissues and structures due to the acid influx, neither of which may be beneficial to the long term health of the fish.
Actually, there is probably a much better way to handle this situation should you ever encounter it without having to use the cola treatment, and that is to simply get your fish into the water, either released back in the lake or into a treated livewell, as soon as possible.
In the case of the former, it has been found that fish blood clots about 35% faster in water than in air. You may have actually experienced this and not realised it. You have a fish with fresh blood running down its side from a wound, yet as soon as you release it in the water you notice little strings of the blood floating around in the water, almost like little strands of gelatin, and not some stream of red like food coloring. This is the blood gelling and coagulating upon contact with the water, most likely from a water-erythrocyte reaction.
In the case of the latter, most livewell treatment formulations have chemicals that act as stress relievers, sedatives, and/or antifungal/antibacterials that will all benefit the fish as soon as he is exposed to them, not to mention the immediate water immersion to speed up blood clotting.
Bass are pretty tough and resilient creatures, and the above tactic may not actually harm the fish. But until we better understand the mechanism for why it seems to work, for most normal hooking instances where a fish is bleeding, a quick release into the lake, or a few minutes of recovery in a properly treated livewell would be my first choice of action.
-T9