I assume you are talking about wireless keyboards, not necessarily bluetooth ones, since I believe there are very few choices for the actual bluetooth PC keyboards. If htis is the case, I can recommend my keyboard, it almost fits your requirements: Microsoft Wireless Comfort Desktop 5050. Function keys are not separated into groups of four, but what I've done is I put sticky dots on the function keys to make them into groups of four. I put bigger dots on F2 and F3, and I put smaller ones on F1 and F4, so that I can feel the whole group of 4 as a single block of keys.
HTH

--Tony