Another great question. I think one reason people think most dreams are bizarre is because those are the kinds of dreams we tend to share with others. If you wake up one morning and remember a dream where you were studying for an exam, or were stuck in traffic, or talking to some friends, you’ll likely not go out of your way to tell others. But, if while stuck in traffic a giant eagle grabbed your car in its talons and lifted you high above the city and flew you and your automobile across the sky, and then set you down by building where you work, then you may want to tell someone! Some people have also argued that by virtue of their unusual and salient nature, bizarre dreams are more likely to be remembered than their mundane counterparts.
There’s also the question of what we mean by bizarre. For instance, bizarreness can refer to likelihood of occurrence of the dream content in waking life, its degree of his adherence to natural laws, or to the presence of discontinuities and incongruities in the dream. Thus, dreaming of seeing someone hit by lightning is certainly unusual, but not bizarre in the sense of soaring through the air like a bird, or experiencing a sudden change in the dream setting (e.g., from being in a park to finding yourself back in a school from your childhood). And things can certainly be “off” in dreams, like seeing your best friend but realizing his voice is that of someone else, or that he inexplicably has no hair, or oddly long and crooked teeth.
That being said, studies of dream reports collected from laboratory and non-laboratory settings converge in showing that for the most part, dreams are a reasonable simulation of waking life in terms of characters, social interactions, activities and settings. Specifically, dreams typically contain the self from a first person perspective, take place in real and spatially coherent commonplace environments, tend to contain realistic recreations of familiar characters (e.g., family members, friends, colleagues) and similar to waking life, are nearly always organized around social interactions with others, including emotional and intellectual exchanges. Thus, contrary to older theories emphasizing bizarreness and disguise in dreams, modern dream research shows that a majority of dreams are best understood as simulations of life experiences that emphasize interpersonal and social interactions.
Of course, that is not denying that dreams can sometimes be very bizarre and that the dreams of some people are definitely stranger than the dreams of others.