Well iim a Judoka && ii see plenty of female Judokas.. after a while they seem fairly happy to have a grapple with the guys aswell, they get used to it i guess. Also, as it's around 60% stand-up and 40% ground (variies from club to club) so maybe for a shy young girl it would be a lil better option compared with BJJ that would be a far higher percentage of full body contact on the ground i.e. grappling. Aikido may be another option aswell.. It all depends what she's seen and been interested in ii s'pose.. maybe tell her to check some martial arts out on youtube..
If you want to find a local club then give them this website address ~ www.cmaa.co.uk its the same governing body I use for my kids karate classes ( not a water down version ~ no hard work then fucking belt ).
Cobra Instructors have to jump through hoops to be qualified to teach under 16's so you know they are above board.