Really? Odd. Have done this for many years since I was a kid and at worse, just have to air out the bag for a while. Then again, I'm not particularly sensitive to the smell of chlorine and wouldn't pay much attention if my bag smelled a bit of chlorine for a while.
The best thing to do (mostly to preserve your swimsuits - letting them sit in chlorine will ruin them quickly) is to rinse the suits out well in the sink, roll and squeeze in a towel, and then transport them home in a plastic bag to rewash and dry. Another idea is to do a more thorough rinse at the poolside outdoor shower (which I will do in a pinch) - this will rinse both your body AND your suit, so win, win.
Or just toss them in a plastic bag and remember to wash and dry upon returning home (I am assuming travel time will be less than 24hrs?). I mean, not much different from my kids going swimming at a friend's house, cramming their wet suits in a bag, and then promptly forgetting about it until the next day when their suspicious mom fishes it out.
Not the best way to preserve suits, but not the end of the world once or twice. I'm a bit more meticulous because I swam 4-5 days a week at our rec centre and quickly got into a routine of rinsing my suits at the sink.