Bittages in images are quite often misunderstood.
The number of bits simply determines how many colors can be in the color pool at once. For instance, 24-bit bitmaps have a color-pool of about 16.7 million colors, and an RGB limit of 255 each way.
Less bits simply lowers the possible number of colors in the color pool. But even a 16-bit image has approximately 11.3 million colors, and about a 191 RGB limit. In other words, the pathetic imaging abilities of a human eye probably wouldn't notice the difference unless the color pool was displayed right in front of them, due to the number of close colors.
Anything that implies '16-bit bitmaps' is basically saying they want a 24-bit bitmap (or higher), and they're gonna strip the colors down to a slightly different set, which you most likely won't notice.
So don't worry about it, just use 24-bit

EDIT: It just occurred to me that I wasn't too clear about how it 'strips down the colors'. Here's an example:
Let's say, 24-bit bitmap color are looked at like this, in numbers:
1 2 3 4 5 6 7 8 9
A 16-bit would strip some of those colors, to make it look like this:
1 3 5 7 9
However, any colors falling on '2,4,6, or 8' would be moved either to the left or to the right (program decides). However, it doesn't matter. The colors are so close, the human eye wouldn't even notice. End of explanation
