I'm guessing that your bottom tiles are on the shower floor? Really, I don't think the grout lines should be turning black in two days in a new home unless you have an excessive amount of heat and humidity in your shower area. If your grout was sealed and no water can get under the grout and grow mold, it should not be turning black so quickly. If your house is new -- have the shower construction checked. The bleach is disguising the real problem; in most homes bleach will clean/remove surface mould, but when it comes back repeatedly so quickly, something else is going on beneath the surface. It's possible that all you need to do is clean with your bleach; let it dry well and seal it. If that doesn't work, get an expert in to check it out before it becomes a more serious problem. Good luck.

1 - use the ventilating fan when you take a shower, until the room is dry.

2 - buy a grout sealant and apply it to the grout according to the directions.

Maybe you can try a stronger chemical cleaner like Hydrochloric Acid that you dilute with a bit of water to prevent grout damage. It's what most professional tile cleaners use, although I'd be very very careful in using this. Wear rubber gloves and have plenty of ventilation.