Hello!
My name is Jozsef Kiraly, and I'm currently a senior student of Computer Science at University College Nordjylland, Denmark. I've been working with web technologies for the past 8 years, including but not limited to PHP, MySQL, HTML5, Javascript and lately Node.js. I've also worked with multiple different platforms, such as Wordpress, PrestaShop, Concrete5, and various other CMS, web framework (e.g. Bootstrap, Boilerplate).
About myself: I'm a driven developer and web designer, who loves a good challenge, and wants to improve himself. I'm also a perfectionist, and a hard worker.
For your project, I'd start with using PrestaShop. It is really widely used, lots of features, I'd say it is to e-commerce platforms what Wordpress is to CMS systems. It also has support for the most commonly used BitCoin payment gate, BitPay.
I don't want to rush forward with a time estimate, as I do not know what other features you might want, but if the major features are the ones you detailed (e-shop with bitcoin payment), I'm sure I can finish it in a few days.
Please, contact me soon, so we can begin working on it as soon as possible!
Yours
Jozsef Kiraly