A simple bubble sort implementation in Java
Bug

On the array { 3, 1, 4, 5, 2 }, the result will be { 3, 1, 2, 4, 5 }. In order to fix this, in the inner for loop change

int comparisons = 1;


to 

int comparisons = 0;


API

The Java coding conventions dictate that sorting routines are declared static, return nothing (have type void), and provide the version of the routine that can sort a particular subarray within an array.

Also, you might prefer to declare the constructor of BubbleSort as private, since that object does not do anything of interesting on its own.

Algorithm

Your algorithm runs always in \$\Theta(N^2)\$, whereas the actual bubble sort runs in \$\Theta(N)\$ on almost sorted input. Refer to the Wikipedia for pseudocode that is more adaptive.

Printing an integer array

Instead of 

for (int iterations = 0; iterations &lt; numbers.length; iterations++) {
    System.out.println(numbers[iterations]);
}


you can easily write

System.out.println(Arrays.toString(yourArray));


Hope that helps.