Command substitution itself runs in a subshell so thats one bash process
your search for bash ($0) i.e. grep -c bash also ends up in the process table at that time so thats another process (grep) containing string bash. Note that, this might not show up in the process table at the time of running, depending on how busy your system is.
And you have two (or whatever) actual bash processes (sessions) running presumably are the rest
You can use a Regex trick to get rid of the false positive i.e. grep one from count:
ps ax | grep -c "[b]ash"
It would still count the subshell while doing command substitution:
var=$(ps ax | grep -c "[b]ash")
So you need to manually remove one from this count.
Example:
$ var=$(ps ax | grep -c "bash")
$ echo $var
4
$ var=$(ps ax | grep -c "[b]ash")
$ echo $var
3
