I think Birdie is a cute nickname.
Bertie sounds more harsh to me (really any "bert" names do).
My vote is for
Alberta nn Birdie or Albie. I agree with you that it's fresher.
But if
Roberta would honor someone important, it might be a better choice simply because of that person.
Robbie could be a fun nn but I also like the nn
Bobbie. I think
Bobbie also emphasizes that it's a girl's name (which may or may not be important to you).