Hello gap,
the share of Bofors and other type of AA weapons may had been rather variable. One major factor was the time (few or no Bofors guns in early war), another the place of refits (British ships rarely received Bofors guns if not refitted in US yards; the US were the primary producers of Bofors guns). I would also guess, those British transports carrying US troops were first to receive Bofors guns ...
Early outfits probably comprised HA versions of 3 inch (either 12 pdr/12 cwt or 20 cwt; the first one was mainly used no smaller vessels so probably not many on troop transports) and 4 inch (Mk. V) guns plus some/few of the older tpye (Mk. II) pompoms. I have no idea if .5 inch Mk. III machine guns were used on transports; same holds for the newer Mk. VIII pompoms. The 20 mm Oerlikons, as the 40 mm Bofors, became increasingly prominent after the US entered the war.
Summary ... much room for speculation and creativity
