The first option that occurs to me is to use a group to limit the ability to have the /run command started.
Eg:
Code:
on *:start:{
  .enable #bot_start
}
#bot_start off
on *:text:*call bot*:*:{
  .disable #bot_start
  run "C:\Internet Utils\mircbot\mirc.exe"
}
#bot_start end

When the script starts, the group #bot_start will be enabled.
This will then allow the call bot text to be recognized.
When that text is recognized the first time, the group is disabled, then the other mIRC is run.
Since the group is disabled the first time the text is recognized, that ON TEXT event will not be triggered again.
Exceptions are:
1) The script is restarted
2) The group is re-enabled, either manually or via another script.