Should the unused areas on the top layer of my RF PCB have ground pours?
RF Engineering is "Pure Black Magic." Proponents will insist it is not, but unless you have a PhD in physics, it probably will seem so. The concepts of resistance, capacitance, and inductance, which makes sense at DC and low-frequency (up to some MHz), are completely skewed when it comes to high-frequency design and implementation. Traces can behave more like resistors or impedance elements, pads and gaps seem like capacitors, corners like reflectors, etc. The full complexities are beyond even a short book on the topic.

The short answer is, "RF" and "2-sided PCB" are seldom heard of together. Most RF (transmitting) devices use a 4 or more layer PCB, and the outside layers are typically ground planes. Some will say this is more to err on the side of caution, but for someone unfamiliar with RF design, it can mean the difference between a working design or not.

For a transceiver device like Bluetooth, near the location of the antenna when transmitting, the electromagnetic field produced can couple to nearby traces (especially as their length approaches a quarter of the wavelength) and induce voltages and currents, causing erratic behavior. That is why ground planes are used; to absorb these waves. Near the antenna the EM is strongest, so they can't be laid arbitrarily there; dimensions and even shape can be critical for correct operation. Further away, it becomes less of an issue, as the EM field dissipates at the inverse square of distance. This TI app note touches on some of the other details at high frequencies.

I'd say the most practical solution is to find a reference PCB layout for the particular BT device being utilized and start from there. Hopefully the manufacturer has made one available. For comparison's sake, here is a small picture of one such design. It's datasheet doesn't mention much about the PCB, likely because the designer spent a great deal of time working on it. The PCB appears as though it could be a 2-sided one, however this is unclear. A larger photo can be seen here. Traces are seen on the top side and you may be thinking "Aaha! I knew 2-sided could be done..." however some tiny but very important things are noticeable:


There are a strip of vias below the antenna. These are closely-spaced to short out all of the strongest EM field to ground.
It's impossible to tell if the left side of the antenna shorts to ground under the silkscreen logo. If it does, it may be a PIFA antenna.
There is definitely at least a partial ground plane on the reverse side, as the majority of the center PCB is dark. As Olin explains in Paul's link above, a few small pads and traces here and there probably won't matter much, but an inch-long trace or group of non-grounded-anywhere-parts is asking for trouble.
The micro-vias seen in some of the front-side traces likely connect to the ground plane. These were not placed willy-nilly, but fill in as much of the top surface as possible to reduce EMI there the best it can. (This is an attempt at trying to produce a robust device without using more layers.) It may be that there are enough top ground areas, covering enough of the surface, that it prevents much coupling there. (Ever wonder why a microwave oven has holes in the door, but no microwaves come through? That's because the holes are much smaller than the frequency (wavelength), so the microwaves cannot penetrate it.)
There are likely traces on the back side underneath the antenna which seem to "do nothing" or connect nowhere. Like squares or rectangles. This is where the really funny business of RF comes into play. Remember at high frequencies, a pad can appear as a capacitor. So those traces are probably designed to introduce some capacitance or coupling physically at that location, even through the PCB. This can be done to "connect" one part of a resonating element (antenna) with another, even though no physical connection exists.