Not everyone likes bikes, not everyone's going to want to ride offroad. Figure out why she's not interested - is she scared of the bikes/quads, does she not like the noise (ear plugs), is she concerned about co-ordination (changing gears with the feet takes a bit to get used to, but it's not a biggie)?
If you can start with that, you can figure out if she's ever going to ride. I posted why I started to ride as someone else asked why we had started, so thought I'd start a new thread (where are the other answers).
Check out Cindy Gross's page for excuses -
http://cindygross.tripod.com/dirtbike.htm and see if that helps any.
Don't force your mum into anything she doesn't want to do, it won't do anyone any favours. We encourage each other & any others who need it here, but if any of us turned round and said "I'm never going to ride again because of ...." we'd accept that (we'd have to really). As for quads, I've ridden one once and to be honest, I hated it, that thumb throttle is horrible to get used to, I prefer the twist sort, just because I feel I have more control over it (that's my opinion, I know others who are the opposite).
Good luck, let us know how you get on, just please don't try and force her, if she's like me, she'll be even more stubborn/determined not to :)