Hi!
I've worked with Bootstrap 3 a lot and I believe I can do this extremely well and fast. I'm only bidding for two weeks because it's the Christmas season and I may not work full-time for a day or two.
But, honestly, if there isn't anything tricky going on with your back-end, it seems like a project that can be done in only a couple of days of work (give or take due to the time zone difference).
As for converting the site to fully responsive, this should be a breeze with Bootstrap 3.
Though, it could be better than simply fitting the screen, if instead of using tables for the lists (watches, forums, etc.), we were to use divs with appropriate classes (I'm thinking list-groups and media-objects).
That way, in mobile-sized resolutions, we could e.g put the description of a watch beneath its image and more-info/save buttons. Or in the forums page, we could put the forums stats beneath the title.
These are my thoughts, contact me if you have any questions, I'll answer as soon as possible. I'm also noting that the hour here at my time of posting is 2:29 AM and I'm calling it a night, so if you want to contact me and I don't respond for a few hours, don't worry, I'll get back to you first thing in the morning.
That's all, thank you for this opportunity and I hope to hear from you!
Edit: My previous bid for two weeks was too much. Christmas or not, this shouldn't take anywhere near that long, so I'm reducing the time-frame to 9 days which still is way more than needed.