You have a Tile class which has a BitmapClass
instance. Perhaps that should be a static property (belonging to the class, not every instance) to begin with. My guess is you're using the memory for the whole tile sheet every since time you instantiate a single tile which you probably don't want to do.
Another thing I'm noticing is you're creating a new BitmapData for each tile, when in fact you probably just need the tile data (it's id/coordinates) so you can copy pixels into the final BitmapData which gets displayed on stage. Perhaps you need to a class to manage resources(embedded bitmaps) and another to manage the different Tile instance(which should hold render data and references to pixels, but shouldn't store the actual data) and copying to the main buffer.
Also, it's a good idea to use BitmapData's lock() and unlock() functions for performance when doing multiple pixel operations on an image.
Have a look at Lee Brimelow's Sprite Sheet tutorials (part 1,2 and especially 3). They're really easy to follow and useful.
Also, it might be worth having a look at the have a look at the GPU accelerated IsoHill library.
I've used IsoHill for a project before and it's quite fast, but it's best to get comfortable with the basics first, otherwise this might seem a bit much.