Well, your description of 'bot' isn't too entertaining, as 'bots' are what the mirc trojans (that do what you are explaining) do. I don't see any immediate reason why you would need to hide mirc completly. If its a problem with running your chat mirc and the bot mirc, and clicking the wrong icon several times, you could do this.
Either make your chat mirc not shrink to the systemtray, or change the icon of the bot mirc. This eliminates the "wrong icon" problem.