Convert BMP to AI

Even though that's not an actual conversion, you can import your .bmp file to Adobe Illustrator, and continue working with it as part of your graphics.

If you have been looking for a method to convert .bmp files directly into vector drawings (.ai files), you will need a moderate understanding of Adobe Illustrator, and the entirety of its key functions. Such a key function is for example LiveTrace, as

However, you may have been looking for a way to create a vector AI graphics from BMP bitmap sources. This will require moderate knowledge of Illustrator and its functions, especially one called LiveTrace as it basically enables a .bmp to .ai conversion. You will, however, need to know what you're doing.

Find out more in the this tutorial Converting Rasters to Vectors Using Live Trace in Illustrator.