I think Beatrix Holly is just lovely!
I also love Pippa Rose, and I think they go really well together. Maybe Pippa is a bit short as a full name in comparison to Beatrix...?
Bea and Pip sound very sweet together!
Here are some other suggestions in case you're not quite decided on Pippa Rose;
Philippa Rose nn Pippa/Pip
Emmeline Rose nn Em (Bea and Em?)
Emily Rose nn Em (Bea and Em)
Heidi Rose (Bea and Heidi)
Louisa Rose nn Lou (Bea and Lou)
Lucinda Rose (Bea and Lucy/Lucie) (like Beatrix Potter and Lucy Maud Montgomery)
Annabel Rose (Bea and Anna)
Susan Rose (nn Sue or Susie)
Theodora Rose (nn Teddy)
Alice Rose (Bea and Alice)
Dorothy Rose (Bea and Dot maybe?)
Matilda Rose (Bea and May/Tilly)
Good luck! :) Very elegant names!