What is the term for a common or potential pun of another word using a misspelling? For example, I thought the made-up word bikery was a funny sort of play on the word bakery. What, therefore, would bikery be called in relation to bakery?
I believe you're talking about a portmanteau, which is where parts of two different words (in this case, "bike" and "-kery", from "bakery") are combined to form a new word.
There's a long list of these over on Wikipedia, including such words as "cyborg" ("cy-bernetic" + "org-anism"), "gaydar" ("gay" + "ra-dar"), and "mockumentary" ("mock" + "do-cumentary").
Some portmanteaus—like those above—become regular words in the language, and can assume either less-formal status ("gaydar"), or completely formal status ("cyborg"); the only distinction is where and how people decide to use them.
So in this case, you've simply noticed an informal portmanteau that "didn't stick".
You could also call it one type of a "linguistic blend" in formal speech, but that would be less specific relative to this example. Essentially, that's what the "pun" of your title indicates.