Nancy is spot on (as usual) that converting Bitmap to SVG automatically is usually a non starter.
The only route I have had any success with this, is to open the Bitmap in Illustrator (I don't know of a suitable alternative but I'm sure one probably exists) and 'Trace' the image to a Vector. This often involves a certain amount of manual input to get the Vector as simple as possible (simpler = smaller) whilst still keeping it crisp and smart. The more complex the image, the more manual input is required, and there is only so much that can be done without resorting to manually recreating the image.
It should be noted (however obvious to some) that there is a BIG difference between Vector graphics and Bitmap images, not least in the way they are created/edited. Someone very proficient in Photoshop can find Vectors extremely difficult to work with, and vice versa.