Filling 2" gap between a tub and existing floor tiles for 30" bathtub in 32" tub opening
2" of tile - after that it's decorating (i.e. try to match and trim 2" chunks to fit of the tile you find that most closely matches the tiles you have; 2" of "border" tiles, 2 rows of 1" tile (perhaps checkerboard-patterned) the options are endless.) Thinset, tile (with or without lots of trimming), grout, possibly sealer. 

A space that small won't really be too time consuming even with all the needed steps. I can't think of a faster way that will stand a chance of lasting and looking decent, but if you want to be the guy that fills it with caulk, I'm not stopping you, simply advising that it might not prove suitable or attractive.