Does a simple bug detector detect electric field or magnetic field?
It detects radio waves – it has an antenna. And: It's completely useless by design.

One thing to realize is that if someone clever was to construct a bug in the year 2016, it's not going to be an FM transmitter generating 100mW of output power constantly; that would both waste power and make it easy to find.

It's much more likely to be a "silent" recorder (you can record years of cell-phone-quality audio on a microSD card...) that can be triggered remotely to transmit its data only when the sniffing party considers it safe to transmit. There's a famous example of a small sculpture that contained a membrane that could vibrate with air pressure – turning it into a audio-modulated RF retroflector when illuminated with radio waves from across the street. Of course, that illumination did not happen while the friendly intelligence service was scanning the room for active transmitters.

So, having one of these is essentially snake oil. This isn't the movie, where you can rush into a room, scan it with a magical electronic device, and declare it "clean".

Another thing to consider is that even when the bug was actively transmitting, it would almost certainly use spread-spectrum technologies. Spread Spectrum is a World War II invention (aka "old news"); it's used to distribute power in a wider part of the spectrum, either to make it possible to make communication more resilient to interference, or to hide the transmission, even below the level of noise that is inevitable in every receiver at room temperature.

Yet another thing to consider is that you need much less power to transmit little information over short distance (like a bug probably does) compared to transmitting much information over large distance (like a TV tower does). In fact, if you are within 10 km of a 660 MHz TV station (secondary, or so-called "low-power") with 15 kW power, you'd get about -28 dBm ("dB Milliwatt", usual unit when dealing with radio communication devices) at where you are. If your bug chose a frequency right between two TV channels, and only needed to transmit 30 m instead of the 10 km, and the bug receiver was as sensitive as 25-year-old cellphones (-120 dBm sensitivity), the signal transmitted by the active bug would need to be 20 dB, or 100 times, weaker than the power of the TV station that you receive at the same place.
 In other words, you can't "see" that bug between the TV stations without knowing that there should be nothing between the TV channels. And even if you knew, TV is just one of hundreds of things that communicate. I have absolutely no idea how you'd go and find an even mediocre clever unknown bug without military/intelligence agency-class automated signal classifiers... 

No matter how you put it, if you need to be paranoid about bugs, you need to live in a copper-shielded hole in the ground, or make mechanically sure the room your sitting is free of bugs and holes through which acoustics could be extracted.

In no case whatsoever is this device capable of doing anything useful.