The code looks way easier to read if you don't use regular expressions.
int count = 0;
for(int i =0; i < string.length(); i++)
if(string.charAt(i) == 'a')
count++;
count now contains the number of 'a's in your string. And, this performs in optimal time.
Regular expressions are nice for pattern matching. But just a regular loop will get the job done here.
