Scottish Rugby Union chairman Allan Munro has already vowed to appoint a permanent national coach before the visit of New Zealand, Argentina and Samoa to Murrayfield in November.
But, after Bulloch retired from the international arena last week, Petrie is determined to leave no question mark over his own position as captain of the team.
He said: "As far as I know, I am still the captain.
"It was Frank who appointed me to start off with, for the interim period against the Barbarians and Romania.
"But I am in possession of it at the moment and it is up to me whether I get the chance to do it again.
"I am in a position where, unless I play well, I cannot guarantee my place in the team.
"So I am very determined to play well enough for Glasgow at the start of the season to first of all get my place in the Scotland side regularly.
"And, if the captaincy comes alongside that, then great. But it is a job I want to keep and I feel I can do well."
But Petrie maintains the appointment of Hadden on a full-time basis would be welcomed by the whole squad.
After Matt Williams was sacked in April, the Edinburgh Gunners head coach was given the post on an interim basis.
Petrie said: "All the players are very happy with the way Frank went about things over the summer and I think you would find he would have the backing of all them.
"Obviously, Frank done a very good job in the two matches we played and you would hope he might get a chance.
"Again, that is something for him and for the management of the SRU to sort out.
"But, hopefully, it will be sorted out sooner rather than later, so we can get a good preparation for the autumn internationals.
"It is going to be a very tough series - we have got three very hard games coming up.
"There is a bit of confidence coming back into Scottish rugby and, if we can get a good start to the season with our professional teams, then there is no reason why we can't do very well in the autumn."