i dont find anything casual about sharing a seat with a girl on an amusement park ride.
its a date bro
take advantage of this as an easy move. rather then the normal stuffty dating most girls want.
she is making it so easy for you, dont puss out because you dont like roller-coasters.
i mean i dislike chickflicks, but ill go to one if a potential date begs me to. when girls do all the hard work, things are very easy
if a current gf wants you to do things you dont like, you must remind yourself that going on a ride to please her is much easier then spending time with her grandparents, or helping her do chores.