I wouldn't bother bringing it directly from AI to DW. AI doesn't save in web-ready formats without using the Export function. You can go to File > Export to export to a .jpg. If you do it this way, you will get the entire art board as "white space"
The better option would be to bring the .ai art into Photoshop, crop out what you don't want and use Photoshop's Save For Web function to turn it into a web-optimized .jpg, .gif or .png.