I'm from Australia, I'm not familiar with the brand you're referring too.. So I'm actually not sure if you're referring to cough syrup containing codeine or cough syrup containing DXM.. Either way, it is pretty hard to OD unless you're mixing it with something else dangerous, but basically when it comes to codeine, your body won't likely even metabolise enough of the codeine into morphine to OD, regardless of how much you took..
Also, bottles come in different sizes, so asking whether or not a bottle is going too be too much.. well, that is difficult to say.
However, if it's your first time and/or you have no tolerance, you probably don't want to exceed 150mg codeine (otherwise you may end up ill / vomiting) and you probably don't wish to exceed 300mg of DXM (otherwise you may end up having a really difficult time determining where your body ends and the rest of the world begins).
Also - regardless of whether you're chasing DXM or codeine, make sure whatever you take doesn't list any other active ingredients; typically they'll be the most dangerous thing in the bottle.. Often there'll be an artificial sweetener or some such thing, typically with a dosage aligned to make you poo watery poo for a while, delicious, runny, murky-yellow shit. Then again, if you have an opiate induced state of constipation, then you can beat this.