The midfielder stepped up to slam the ball past Jussi Jaaskelainen in injury-time after Abdoulaye Faye was adjudged to have handled the ball in his own area.
Bullard's spot-kick cancelled out El-Hadji Diouf's penalty to give Chris Coleman's Fulham their first point of the season, and it was no less than they deserved.
However, it was Bolton who nearly took the lead in the fifth minute when Ivan Campo's pass found Kevin Davies in space. But he was denied a clean strike at goal by Franck Queudrue, who made an excellent recovery tackle.
At the other end Brian McBride repaid Coleman's decision to start him up-front at the expense of Collins John by almost putting Fulham one up with 13 minutes gone.
The American World Cup star connected with Bullard's curing free-kick but could only direct his header into Jaaskelainen's hands.
Bullard was again looking dangerous from set-pieces three minutes later when his free-kick, this time from the left, somehow eluded both Ian Pearce and Heidar Helguson at the far post.
A superb flowing move almost gave Fulham the advantage in the 28th minute when Luis Boa Morte and McBride combined well to play in Bullard, but Jaaskelainen saved his deflected shot.
After the restart it was Fulham who looked again to be the most creative side. Liam Rosenior's pass was perfect for Helguson, but the Icelandic international planted his header wide.
Kevin Nolan nearly capped an excellent performance with a goal in the 54th minute when he latched on to Diouf's pass. But he was denied by some last-ditch Fulham defending, with Pearce hacking the ball to safety.
But it was the home side who stamped on the gas and Michael Brown was left cursing his luck on the hour mark when he fluffed his header from close range when he should really have scored.
Boa Morte then saw his shot blocked before Helguson fired wide as Fulham were left ruing their missed opportunities.
Despite all their efforts, the hosts were punished when referee Alan Wiley adjudged that Boa Morte had fouled Gary Speed in the box.
It was harsh on the Fulham captain, who was at his brilliant best, but Wiley did not hesitate to point to the spot.
Diouf converted the spot-kick, sending the ball high into the net and leaving Niemi stranded 17 minutes from time.
But just as Fulham thought they had been caught by a sucker punch they were handed a lifeline when Wiley awarded them a penalty in the 90th minute.
This time, second-half substitute Faye was ruled to have handed the ball in his own area. Bullard stepped up to send the ball flying under Jaaskelainen from 12 yards to earn Fulham a share of the spoils.