How about a military officer meeting the Tsar for a private audience indoors?
There was not such thing - "private audience". All Tsar's encounters with his subjects were considered official and maintained as such. Russian emperors almost never gave individual audiences to officers or other government servants other than ministers and members of the imperial suite. The latter included hundreds of generals and officers each of whom had the theoretical right to request a personal audience - but had to consider it very carefully, unless such an audience was not directly warranred by the court and military regulations. Otherwise one risked not to find his name in the Court Almanach upon its regular New Year update.
When an officer was invited by a palace servant to the Tsar's study, he was already bareheaded. If prior to the audience he was on duty at the palace (commanding the guard shift, or as a fligel-adjutant etc.), he was keeping his cap or other headdress on his bent left forearm and greeted the Tsar with a "military bow". When acknowledged by the Tsar, the officer had to approach him and to bow again, in response to which the Tsar usually extended his hand - to be shaken lightly but firmly with yet another bow.
If the officer came to the audience from outside the palace, he was expected to leave his headdress and sword at the cloakroom. Otherwise the ceremony went as described.
When an officer (e.g. member of the palace staff) met the Tsar occasionally in the palace, he had to stand at attention, to bow, to wait for a few seconds and then to proceed on his business. When the Tsar (or actually any other military superior) entered a room where three or more officers were present (but no ladies), the senior officer commanded "Genlemen!", and everybody stood at attention until greeted by the superior.