You have a doSort() method, but it is never called... in fact, there is no draw() function!

I am a fool.  Thanks for pointing that out!  It's working fine now, though it is really slow. 

Agreed regarding doSort().  draw() is not really needed here, though.  

I would like to add a few comments to this:

1. Conceptually, I enjoyed thinking about your program...sorting the pixels of an image.
2. It was a little tricky trying to figure out some of your code because your bubbleSort() function had three parameters.  Two of the parameters weren't really necessary.  All you really need to pass to the function is the array itself.  If you need some variables in your bubbleSort() function to help you with the sorting, then declare those as local variables, within the function itself. 
3. pixels is a one-dimensional array containing all the pixels you want to sort, right?  Since that is the case, it's simpler to rewrite this loop:

Sorry, one more thing.  I see that Processing has its own sort() function.  Have you tried it?  I tried the following (and used reverse() because it seems you wanted to sort from brightest to darkest...without reverse(), it gets sorted darkest to brightest):

Ah, I thought the point was to show the sort in real time, like one sort operation per frame!...

Funny effect:

1. PImage img;
2.  
3. void setup()
4. {
5.   size(100, 100);
6.   img = loadImage("G:/Images/map.png");
7.   image(img, 0, 0);
8. }
9.  
10. void draw()
11. {
12.   oneSortStep();
13. }
14.  
15. void oneSortStep()
16. {
17.   loadPixels();
18.   for (int i = 0; i < pixels.length - 1; i++)
19.   {
20.     if (blue(pixels[i + 1]) < blue(pixels[i]))
21.     {
22.       // Swap pixels
23.       color c = pixels[i];
24.       pixels[i] = pixels[i + 1];
25.       pixels[i + 1] = c;
26.     }
27.   }
28.   updatePixels();
29. }

I used a small image because it is slow enough!

Hi aferriss, I have spent a lot of time and energy on sorting things over the last few years, much of it in Processing and with images (see: http://www.jeffreythompson.org/RandomHexadecimalValuesSortedNumerically.php).

A few thoughts after you resolve the tech problems:
+ The color model you use will result in really different results - ie: the way RGB is stored vs hex vs HSB.  Generally, HSB is favored for data vis because it gives clean shifts across the spectrum
+ If you really want to geek out, check out the video " Sorting Out Sorting" - it's a 30+ minute early computer animation of different sorting algorithms.  Super nerdy and I love it!