If the mirror is bent, a level will not help. A level is useful if orientation relative to gravity is important (something has to be horizontal or vertical, like a cabinet, counter, or picture). That isn't even remotely relevant here. You could do this measurement while staying at the International Space Station.
Even cheap mirrors from a dollar store are more than good enough for this, as long as they are glass. Most plate glass glass is made by floating melted glass on a bath of molten metal (which is heavier). The molten metal, if undisturbed, provides a perfectly level surface.
Just don't use a plastic mirror, or a cheap polished metal one, not to mention a magnifying mirror.
Even fairly noticeable distortion will not matter at the distances involved in this measurement. Let's say that your mirror is so horribly warped over the tiny ~65 mm pupillary distance that the pupil-to-ruler lines of sight are an entire degree away from being parallel. The measurement will then be off by about 1.7% of the distance from your pupils to the ruler. If you get your eyes within 15 mm of the ruler, the error is only about 0.25 mm; below what you can resolve with that ruler.
If the mirror is fair, but tilted, the effect is negligible because the lines of sight remain parallel. The measurement is diminished according to the cosine of the tilt angle. For a rather significant five degree tilt, it will be only around 0.25 mm short.
