Hello,
When having a bird bath the best thing to do is to empty and clean it regularly. You can clean your bird bath with one part distilled white vinegar and 9 parts water. Simply empty, spray and wipe out, then refill. It's best to dump and refill the water every 1-2 days. It is important to make sure to regularly clean out your bird bath to prevent disease. Not cleaning your bird bath regularly could be detrimental to your birds health. Here are a few links with additional info on bird baths.:
If you are regularly cleaning your bird bath then algae build up shouldn't be a major problem.
In regards to additives to your bird bath like lavender or rosemary, it is best to be cautious, especially with essential oils or cleaners. Birds have waterproofing oils on their feathers that help keep them dry. If you are not careful, cleaners or oils in your bird bath could harm the birds and prevent them from being able to maintain their feathers and health.
In summary I have no knowledge on rosemary specifically, but cleaning your bath regularly should prevent the need to put additives into your bird water and is best for your birds health. Additives can be harmful and its best to avoid using them when possible.