As far as I know, bathing a guinea pig too often is a bad idea. Keep in mind a guinea-pig is a very sensitive pet, if you do that, you'll probably be harming their natural skin protection, which will lead to illnesses. If you really have to, I'd recommend bathing them once at month at most. Even if you don't believe it, guinea pigs are very self cleaning and they take care of it! They spend a part of their day just cleaning themselves.
The hay is an absolutely basic element in their life, as they use it for many things, but the most important is their digestive properties. In normal circumstances, a guinea pig will eat big amounts of hay per day. Additionally, they may use it to "decorate" their bathroom, and also as the base of their bedroom so they are more comfortable.
The best thing I'd advice to do is cleaning the cage every 3-4 days (more often would also might be harmful). Don't worry if they pee on the same place they sleep - but as I read your question, it seems you're not putting any base/substratum? If so, this is very important, in pet shops they sell several types of substratum that additionally absorb smells and makes your guinea pig more easy to live in their cage. Another option is putting the hay as the base of the cage, it'll probably like it more to your guinea pig, but it doesn't absorb smells and plus if you're allergic... Ask at the shop!