In an interview with BBC Sport Bully revealed he had teamed up with former Aston Villa and Derby boss John Gregory to go for the post in December.
Instead Hoddle was appointed on a six-month contract, but his long-term future remains in doubt.
"We would have made a great team and if Glenn does go we'll put our hat into the ring again."
The 39-year-old former England striker believes the club should sort out the situation as soon as possible to end any uncertainty.
Bull, who scored more than 306 goals during his 13 years at Wolves, added: "The best thing to happen for the club would be to stabilise the manager's position permanently.
"If someone is only here for a limited time then the fans become unsure of the situation, and everyone else at the club does, including the players.
"Glenn's done a good job, but we've drawn 10 out of 13 games, which is a lot.
"He has got them working at the moment, and has them playing as a team but he has got to start turning those draws into wins.
"He is a good manager. If he can get the players playing for him at the end of this season, and stays, then who knows what they can do next year."
If Hoddle does go, veteran Wolves midfielder Paul Ince has already been touted as his possible successor.
But Bull, who currently runs his own company as well as doing PR work for Wolves, believes he has the credentials for the post.
He said: "If Paul Ince is in the reckoning then my name is in the reckoning because I've had as much management experience as him.
"With John and myself, I'd have an experienced manager to teach me all the ropes.
"Then if he leaves three or four years down the line, you step in having learnt all the tricks of the trade.
"That for me is the only way for me to get into a club to learn management.
"In football it is who you know and not what you know sometimes.
"If you know a good chairman out there who will trust you and believe you when you talk about your plans for the club, then you have got a very good chance of starting."
In an interview with BBC Sport Bully revealed he had teamed up with former Aston Villa and Derby boss John Gregory to go for the post in December. 
