If the Will relieved the Executor of posting bond and filing reports then he is not required to be bonded or to provide accountings to the Court. However, a wise Executor will communicate with the beneficiaries and let them know the status of the estate.
Under the law the Executor has six months to determine what the estate assets and liabilities are. If it has been more than six months since the Letters Testamentary were issued to the Executor then you may want to ask the Executor, in a nice way, to provide an accounting so that everyone will know what is going on and so that there are no surprises later.
Without bond means the executor has not been required by the court to post a bond with the court to insure that he does his job. Likely he also has been relieved of a duty to do inventories and accountings to the court. While executors do not have to tell heirs everything, if you are an heir and feel the executor is not giving you timely information, informally ask. If more than a few months have elapsed with no information, ask in writing. If you haven't heard anything after six months, or feel something wrong is going on, see a lawyer.