Bahdubaday seems to be the word Anna has decided to use to mean TV (of course?!)
Granted, it doesn't sound much like TV or telly but we've got to the bottom of it now.
Léon doesn't really watch much TV, but when he is tired or if he wakens up too early to be sociable, he often creeps downstairs and asks if he can watch an episode of Balamory. Because Anna hears Pudge asking to watch Balamory, as opposed to asking to watch TV, Anna thinks that Balamory is the word for TV. And of course Bahdubaday is her attempt at Balamory. So when she asks for Bahdubaday, she may indeed want to watch Balamory, but she may also want you to put on her Danish DVD of Kaj and Andrea. It's quite simple really...
I'm away to write an English-Baby, Baby-English bilingual dictionary now!