Can addresses controlled by the same key be grouped by another party?

Given that numerous accounts/addresses can be generated with the same key, is there a way for an observer to generate such a list also?

E.g. Bob runs a company and wishes to accept payments in Ether. He plans to make use of a new account and address (but with the same private key) for the receipt of each payment. Tim sends Bob a payment at address A, which Bob has given to Tim.

From knowing address A, is it possible for Tim to generate a list of Bob's other addresses and view his other customers' transactions?