Providing things (baths, feeders, houses, etc.) for birds without having to monitor/clean them often is tough. I'd concentrate on where your water intake is and see if you can place a filter of sorts at this point - one that is easy to change out or clean regularly. We gave up using bird feeders and now toss our seed into a blue spruce - we couldn't clean the feeders enough to make them safe for the birds. You might even have to go to a different sort of bath/fountain that is designed more appropriately for just the sort of situation you are encountering (which, unfortunately, one doesn't learn about until after the fact).

I covered the intake holes in the fountain with fine screening to keep all animal and bird poop out and leaves too. I siphon the covers regularly to clear them. I decided the fountain was for our enjoyment not birds and other critters! So, I put 1-2 1" chlorine pellets in whenever they disolve. The fountain is clean and nice and pest free!