Does cgminer have to be on for me to solo mine for bitcoins I see my antminer has cgminer built into it.
Do I need to have cgminer on my computer screen while "solo mining" for bitcoins ? or can I just have the antminer on and hashing straight through the router ?
cgminer is just the client software to control your ASICs. Where cgminer gets it's work from is your question and that depends ... 


You can run your own full node and point your hashing power there 
or way easier would be to just use some hosted solo pool like http://solo.ckpool.org/


On the website you finde further information on how to solo mine.