Your blood type is determined genetically and your genetics do not change during your life time.

Type O is recessive, so for a person to be that type he/she had to inhert "O" from both parents.
Although the mother type is B, her "genotype" is really BB or BO but since B is dominant that is what shows up in the blood type test.
The type A father would be AA or AO. (A, like B, being dominant over O)

In this scenario, for the child to be type O (really OO)the mother had to be BO, the father AO, and the child inherited an O from each parent.

A and B are not dominant over each other, so if the child inherited the A from one parent and the B from the other, the child's type would be AB.

The + and -, which is the RH type, is inherited independently from the ABO blood types. The above parents could have had an O- child as well (as well as B+ or B-, A+ or A-,AB+ or AB -)