I made the chart by searching for usages of the word in the "scripts" of every episode of Bones. I hesitate with the word "scripts" because these were not official scripts — rather, they were fan-written. (I spot-checked a few and they are, for the most part, pretty accurate.)

As you can see, Seeley Booth (David Boreanaz) dominates the usage of the word "bones" across the entire series — he accounts for 1,867 of the 2,668 total mentions — and almost exclusively uses it to address the character Bones (Emily Deschanel). The few times each season he uses the noun to speak about actual bones all tend to come in one episode, where he gets caught in conversations that practically require him to talk about bones (something he seems wont to do), or when he's telling Bones to go back to examining bones. In fact, he's basically the only character who calls her "Bones" (it is his nickname for her, I guess) except for a handful of instances. Bones herself basically only says the name "Bones" in this context: "Stop calling me Bones!"

"Bones!"

Looking at the data in another way, you can see how the frequency changes over the seasons. It peaks in seasons one and four, and trends lower and lower as the series progresses:

Some caveats. For one, manually searching through every script of every episode of Bones was a dizzying affair, so while I stand by the results, I am not willing to bet my life on the exact numbers. What made this problem worse was that, for some inexplicable reason, the "scripts" from seasons six through 10 only sparingly told you who was saying what at any given time. This meant I had to use my powers of deductive reasoning to figure out who was speaking with each mention of "bones." (Luckily, by the sixth season of scripts, I had gotten a hang of the patterns. Temperance "Bones" Brennan rarely mentions her own nickname — mostly because she hates it — and is always the one talking about how the bones need to be cleaned.) I would give the numbers you see a margin of error of +/- 5 for each season's worth of data.

Also, I originally planned to include more individual characters. (Zack Addy, the nerdy assistant to Bones who disappears from the show's plot after a few seasons, very strictly uses the noun and never refers to her as Bones. Bless his heart.) [Ed. Note: I have just been informed by Ross Miller that Zack Addy apparently became some sort of serial cannibalist and I totally didn't realize this.] They wound up being too varied, however, and their individual numbers paled in comparison to the likes of the main characters Booth and Brennan.

A few things I learned from this: