I don't think the bitmap is necessary at all so if it reduces file size significantly then I say drop it. Also, like I said, zipping the EPS or AI will greatly drop the file size.
I am not sure how familiar you are with Illustrator, and I was unsure if your comment about vector was just a general comment or a comparison of Corel vs Illustrator. Either way I thought I'd mention that Illustrator is a vector drawing program. It's the industry (graphic design) standard for vector graphics...though MUCH more expensive than Corel.