Your tamagotchi will leave 24 hours after the Adult. No, you can't Bump, it is against the rules. When it's mid-night your tamagotchi will sadly leave your Baby. But, you will start on the next generation!
For Example:
If you made the baby at 5:00 P.m., wait the next day at 5:00 P.M. and set it to 11:59 P.M.
Yes, that is correct. Your Tamagotchi Adult will leave the baby in twenty-four hours from the time it had the baby at first. This usually means about two full days for the process to begin. I suggest not pausing your Tamagotchi during the period, in order for you take care of your new Generation!