The bacteria will actually live any and everywhere regardless of there being a filter or not. All the bacteria need is a source of food (ammonia for the one strain, and nitrite for the other) and a place to live. I've actually had unfiltered betta bowls that were "cycled." I simply avoided any scrubbing on the inside during water changes and managed to maintain the colony well enough that I only had to change the water weekly just to keep it clean and remove the small amount of nitrate that resulted from the biological cycle. The water never showed any ammonia or nitrite even after the week - and then once I after I removed a betta (I really only kept the bowls for QT) I tested it just for fun - putting a drop of ammonia in every few days for almost a month, then tested the water - 0 ammonia, 0 nitrite, nitrate off the charts. A consistently active biological cycle in a 1g betta bowl with no filter, no substrate and no airstone. I gave this water to my house plants, who were probably thrilled at the nitrogen.
But that being said I would still always recommend a good filter. And no, you don't need to seed it unless you want to jumpstart. With the fishless cycle you'll get the bacteria naturally over time. Some cycles take longer than others - and make sure that you never add any chlorine to the system with water changes - a system that is just getting started will be killed almost immediately with even the slightest amount of chlorine.
Just add the ammonia every few days - a very small but steady amount. Wait a few weeks before even trying to test it. With luck you'll see the ammonia gone and nitrite appearing or maybe even also gone with nitrate appearing...
