Yes, mold can absolutely be removed from the grout in a shower. It is all a matter of what solution you use.
Most people will use bleach...
....and that's not a bad thing in this situation.
But one of the the biggest misconceptions is that bleach kills mold and this just not true.
So why do I say it's not a bad thing?
Because although bleach does not kill mold it will take out the appearance of mold.
What I recommend is a process that we call the Vinebleach Papertowel Method to remove mold from the bathroom.
You will need 6 different items
1.Bleach
2. White Distilled Vinegar
3. Rubber Gloves
4. A Cup
5. A straw or spoon
6. paper towels
You will then pour 1/2 a cup of white distilled vinegar and about a quarter cup of bleach into the cup and mix it well for 30 seconds.
Then with the rubber gloves on, dip a rolled up papertowl into the solution and apply it to the area in the shower that has mold.
Let it sit there for 4-6 hours and wa la!
Your grout should be much cleaner!