If you want to see if a mirror is two-way or not, put your cupped hands to it and look through them. If you block out the ambient light, you'll be able to see anyone on the other side, as long as they're not in pitch darkness (which they can't be, actually; even if there are no lights on the dark side of the mirror, it will at least be illuminated by the photons coming through it from the light side).
If the dark side is very very dark, then you can illuminate it with a flashlight through the mirror. You may need a friend to hold the flashlight, or an improvised shade you can use one-handed, to do this.
A mirror with no glass in front of its reflective layer is not necessarily a two-way mirror. It's a front surface mirror, all right, but that front reflective surface may be backed by an opaque layer, just like the reflective surfaces in regular back surface mirrors, which have glass in front of the reflective layer.
Most mirrors, including two-way ones, are of the back surface type, because the glass in front stops the reflective layer from getting scratched, or corroding. Front surface mirrors are delicate; delicate things do not last long in hotel rooms. Or in police interrogation rooms, for that matter.
What makes a mirror one- or two-way is its transparency. Without a backing, the thin reflective layer of a modern mirror is likely to be almost as see-through as mirrored sunglasses. If a mirror is reasonably transparent, it can work as a two-way mirror if there's someone in a dimly lit area on the other side of it. The reflection of the person on the lighter side of the mirror is so much brighter than the image of the person on the darker side that it drowns it out. It doesn't matter what side of the glass the reflective layer is on.
Ordinary glass windows work quite well as two-way mirrors, at night. If the lights are on inside and there's no illumination outside, the people inside will see their own reflection in the glass, but people outside will be able to see in. In this case, the glass is working as a front and back surface mirror, since there's no special reflective coating at all.
If you want to conduct some two-way mirror optics experiments of your own, try using compact discs that aren't printed all over their label side. CDs are highly reflective, but also moderately transparent - actually, some of them are very transparent. You can see your face in them; you can also see a lamp through them. And it doesn't matter which way round you hold the CD.
Reference regarding the front-side-equals-two-way myth: