From what I understand, this version of the Arc mouse is NOT bluetooth (buried in the description is a note that it isn't bluetooth and requires a dongle). I bought the black surface edition (refurbished) and 'love' it. It fits perfect in the carrying case I have for the Surface and works on any physical surface I tried. Hotel room desktops to the top of a seat at an airport terminal. There is a lighter colored version that now states Surface in the description that is a few dollars less.
I have read some reviews and a lot of people seem to have problems with the connection which seems to get lost from time to time. Do you have experienced something like that?