Looking at Tamron's site, it appears that this lens was designed for APS-C size sensors (which Nikon refers to as "DX"), and contains an in-lens autofocus motor. Nearly all Nikon lenses with a similar AF motor carry the "AF-S" designation, and it appears that Tamron is using "BIM" to indicate the same.
Therefore, I think you can infer that Nikon film bodies that accept AF-S lenses with all of their related features will also work with this lens, with one caveat. Given that the lens is designed for the DX sensor size, photos you shoot may not fill the frame throughout the zoom range. You might have some success at 50mm, but at 17mm, your shots will have a cool "periscope" effect. :-)
I believe that Nikon's digital full frame bodies will support DX lenses with a special "DX mode", in which the camera deactivates a portion of the sensor.
If you're looking to get a film body, you might want to take the plunge with the film equivalent to your lens, the Tamron SP 28-75mm F/2.8. It's more expensive, and will give you a different focal range on your digital camera, but it is a fast zoom and will work with both DX and FX-sized sensors.