Having my bstore show under my own URL

Is it possible to set up my store so it shows up (to customers) under a different URL? I'd like to establish my own website with my own URL and have the bStore be only a part of the whole experience. It something like this possible? I don't feel like I have enough control over how my site is listed and shows up in search engines. Additionally, I can't control advertising on my site, have a blog, or add additional content as it is now. A drop-ship service like Bravisa works well for me to sell products because it is less work, but I'd like more control over content and the ability to bring customers to my site. (I think people are less likely to buy when the URL says "bravis.com/bstore/mystore) that if the URL was simply the name of my store. thanks