There is surname BEDNARIK as well as BEDNAR.
The ending "ik" on the end would suggest [small, diminutive]http://www.polishroots.org/Research/SurnameSearch/Surnamesen...
Suffixes with a -k- generally began as diminutives. In other words, Jan is the Polish form of "John," and Janek or Janko is much like "Johnny." English, however, typically has only a couple of diminutive suffixes, -y or -ie. Polish (and the other Slavic languages) have tons of them. Most have a -k- in there somewhere, or the-k- has been modified by the addition of further suffixes (e. g., -czak, -czyk). As a rule, in surnames a suffix with -k- means something like "little" or "son of."
Thus Jan is "John," Janek or Janko is "little John, Johnny," Jankowicz is "son of little John," Jankowo is "[the place] of little John" (or "of John's son"), and Jankowski is "from the place of little John or John's son." You see how different suffixes can combine to add layers of meaning to the basic name?
The original usage of these suffixes was to indicate a diminutive form. But they also came to be used in other ways, usually meaning "associated with, related to, exhibiting the quality of." Nowak comes from nowy, "new" + -ak, to mean "new guy in town," and Stasik means "one associated with Staś" = "kin of Staś."
Also, these suffixes were often added to nouns to serve as a term for a person or object perceived as related to whatever the base root meant. Thus Bartek started as a nickname from Bartłomiej (Bartholomew), and meant "little Bart, son of Bart." But once Bartek existed as a name, it could come to be used more loosely as the noun bartek, which means "yokel, peasant, hick from the sticks." This happened because folks perceived Bartek as a name popular primarily among people in rural areas, so it came to be used as a common noun for such a person. We have done similar things in English; you might refer to a redneck in general as a "Billy Bob" or any other name perceived as common among rural folk.
Similarly, sowa means "owl," and sówka, literally "little owl," can be a term for a specific kind of owl, Athene noctuae. But it's also used as a term for the Noctuidae family of moths. Apparently something about those moths reminded people of little owls, and the term stuck. Thus you have to be careful when you interpret surnames with these diminutive suffixes: the "little X" may be turn out to be a term for something not readily apparent. If you trace the development of the name