The cost of left out join versus a select
If you already have the PK value of a certain row in A, a simple SELECT is the fastest possible way:

SELECT * FROM b WHERE a_id = ?


If you need to retrieve a_id first, a join is your best options. Make that a LEFT [OUTER] JOIN only if there can be cases where there are no matching rows in B and you still want a_id in that case (or whatever, you didn't clarify).

SELECT a.a_id, b.*  -- often you don't need all columns
FROM   a
LEFT   JOIN b USING (a_id)
WHERE  a.some_column = ?;  -- not defined


One integrated query is typically faster than two separate queries. LEFT [OUTER] JOIN or [INNER] JOIN perform about the same here.