Should I have an overflow bottle?

some cars didn't have overflow bottles, they just ran the hose down the side of the rad, like Yours. You might get a different rad cap...up to 16 pounds and see if that stops it or install an aftermarket bottle, as I did on My 72 Demon. (chrome looks cool) If that little bit of spit bothers You then I would install a bottle, but also make sure the fan is positioned correctly in the schroud.