Oh yeah, this is a tricky one!
Bywać is indeed a frequentative variant of być. The frequentative is not very common in Polish, and only applies to a few words. I think bywać plus the four words listed on Wikipedia (jadać, widywać, pisywać, czytywać) are responsible for most of its use, if not all.
How does it work? Compared to the regular form, frequentative verbs such as bywać or jadać suggest that something is only true in certain conditions, or that something only happens sometimes.
An example to illustrate this better:
Ich dzieci są niegrzeczne. = “Their children are naughty.” (probably always)
Ich dzieci bywają niegrzeczne. = “Their children are sometimes naughty.” / “Their children can be naughty (sometimes).”
Here the difference is quite stark, but it’s not always that clear.
Sometimes it’s very minor, making the choice between the two variants mostly a matter of preference:
Często jem pierogi. = “I often eat pierogi.”
Często jadam pierogi. = “I often eat pierogi.”
Language purists might say that the latter is more correct (since it better communicates the “habitual” aspect of the sentence), but many people don’t care that much and just say “jem” instead.
As you’ve probably noticed, using both często and jadam (which itself carries the meaning of “sometimes” / “often”) next to each other is a bit redundant, but many fixed expressions are built this way. “Jak często bywa” is a good example of that.
If you take away często, jem pierogi vs. jadam pierogi will have quite different meanings. The default interpretation of the former will be “I am eating pierogi” (though “I eat pierogi” is also probable in certain contexts). The latter will always mean “I (sometimes) eat pierogi”.
I don’t think people often say jadać alone, without supplying it with an adverb of frequency like rzadko, czasami or często. Note that it’s also perfectly okay to say rzadko jadam (“I rarely eat”) or nigdy nie jadam (“I never eat…”), so it’s not like the verbs are restricted to frequent events.
And last, a quick example with widywać:
Widuję go z moją sąsiadką. = “I often/sometimes see him with my [female] neighbor.” (this usually implies a romantic relationship)
All in all, I’d say being aware of the difference is pretty important (especially for “bywać”, “jadać” and “widywać”, the others are used very rarely), but if you can’t get your head around when you should use the frequentative forms, you should be just fine sticking to the regular ones.