The only realistic way I can think of is to connect either yourself or your bot to the IRC network via a Bouncer (BNC) or PsyBNC. For this you would need a Shell Account - you might like to search Google
. (99.999% of the time these cost money). With these you may set a virtual host (vhost) on you/your bot, which *hides* your IP (it doesn't CHANGE it).
If BlabberNET allows 2 IP's then you should just use it - it's not doing any harm to anyone. If the server you're on is giving you a message "Too many connections from this host" (or similar) then try another server - it's possible that not ALL of them are as strict as that particular server. For more server names try /links
or if that's disabled, try the networks website or #Help channel.