LamieRobertson
Not awoke
I don't think there's a limited number of bottles (I imagine a parent bringing a couple of kids might have a couple of bottles), but bags are limited to a4 size, so here's only so much you could carry, and I imagine carrying a more than a couple of lidless bottles would be quite difficult without spillage. But I'd imagine you'd be allowed to bring in two (leave the lids on until you get to the stadium, of course).
I'm pretty sure someone (bozza?) mentioned there being a water fountain in at least one stand, so refilling may be an option, but I've not seen the fountain myself so can't guarantee.
Plus you can ask for tap water (same as what would come out of a fountain?)