There is a MOD out on bbCode permissions. But that selects what group can use certain bbCodes. I don't think there is a MOD on which styles can use certain bbCodes. You could edit the bbcode template and list only the bbCodes you want the mobile style to use. But I'm not sure if the user could still manually enter in a bbCode that isn't listed. Try taking out the bbCodes you don't want and see how it works.
Although what you would need is for certain bbCodes not to show in the mobile style, not the ability to post a bbCode. I would think that the edits needed for that would be in the viewtopic.php file. We would need a MOD for that. That is something over my abilities.[ Post made via HTC Inspire]