My Father's Blood group

Your Father could be A or AB not O .Have a look at this calculator . I don't think the one you used is working properly. http://www.biology.arizona.edu/human_bio/problem_sets/blood_types/btcalca_popup.html
You inherit one set of chromosomes from your mother and one from your father. So you have two sets.

The ABO blood group system is determined by a gene on chromosome 9.
Your DNA can code for A or B or O. We call these different versions different alleles.
As you get one chromosome 9 from earch parent you could receive
A+A,A+B,A+O,B+B or O+O
A sticks certain 'sugars' onto a blood cell ( really glycolipids but I'll call them sugars You may also hear the word antigens)
B sticks different sugars onto a blood cell
O doesn't stick any sugars on.

As your mother is B
She must have at least one B allele (ie version).
The other chromosome can't be A because that also sticks 'sugars' on and if it were A she would be AB
The second chromosome could be either another A or it could be an O .
BUT You are an A
Your mother must have given you an O (if she had given you her B then you would have been AB)
This means your mother must have had one chromosome with a B allele and one with an O allele

Your mother : BO You AO
Your A allele must have come from your father.
He could have A+A and given you his A (and would be blood group A)
He could have A+O and given you his A (and would be blood group A)
He could have A+B and again given you his A (and would be blood group AB)
And you can't tell which he is without testing.

This is a very interesting , I have never even thought about it, but I know I am B+

@Robinredbreast
That means that at least one of you parents must have been blood group AB or B. At least one of your parents would be rhesus positive. . http://www.transfusion.com.au/blood_basics/blood_groups/inheritance_patterns

I am b negative and my dad is o my mum doesn't know what she is