To arrive in the bladder, the CO₂ would have to be absorbed into the blood stream first. Which it isn't, it is just burped out from your stomach. Also, CO₂ which is dissolved into the blood stream is removed through your lungs, and the blood CO₂ level is very tightly controlled by various regulators and reflexes. You would know instantly through your suffocation response that your blood CO₂ is elevated.
A lot of carbonated water gives me gas, especially when not eating enough. But I am not sure it is an issue. People have various gas levels, it just goes in and out.
I always considered drinking a lot of sparkling water an antipattern. I think this is connected with microbiome or people who I knew and who abused the sparkling water. I'm refraining myself from such activities because of the same reason (gas) but I also am sick (SIBO or another inflammation, have to hit diet hard)