I have two freshwater aquariums and I change out water twice a week. I fill a spray bottle with the water to spray my tillansias, and also hold the water aside in a tank for soaking the tillies. I've been doing this since Sept 2012 and as far as I can tell, the plants like it. If you don't have a freshwater aquarium, maybe you could use a very, very diluted fish emulsion, available in garden sections of many stores; just read the ingredients first. I suggest diluting a lot because I don't have many fish and the plants in the aquariums also use a lot of what the fish and snails, um, discard.

Looks like T. Loliacea.

Some "faster than others" include T. x Nidus which is a natural hybrid between Ionantha and fasciculata. T. mitlaensis and paleacea are two other species. Once mature, many species seem to grow faster and larger when actually they are just adding on to the core of spent plants. So patience is the key for most but the above 3 are my picks.

I, too, live in an apartment though it may be a little larger than yours. I have some small, almost ball-shaped ionanthas; they may be druids (I used to be sloppy about labeling things; I'll have to wait to see what comes when they bloom again). This recent summer I invested in some T. neglecta, and they are quite small but full of character. Ball moss (recurvata?) is small but can act rather like Spanish moss, clumping and getting larger. I also have what I think is a mini aeranthos, or maybe better described at http://www.rainforestflora.com/store/tillandsia/A20020/aeranthos-Miniata/ However, like ball moss and many others, individually the plants are small but they may grow fast and clump together. But in the world of Tillandsias, "grow fast" is at best leisurely, sometimes in the order of years, so you may have more to choose from than you realize :) .