The Red Devils are due to tackle Manchester City at Wembley on April 16, with Bolton taking on Stoke the following day.
All four teams will take a similar route down to London for the encounters and will be joined by Liverpool fans, whose side face Arsenal at the Emirates Stadium on April 17.
In addition, hundreds of thousands will line the streets of London for the annual marathon, prompting a warning from Ferguson of “absolute chaos” in the city over the weekend.
Ferguson added that the situation is “quite incredible”, and Bedford has suggested the only way to ease the United boss’s concerns would be for the FA to move its events.
“Our date is established well in advance and agreed with all London agencies involved,” he said in a statement to Press Association Sport.
“There have been clashes in the past with other events at Wembley and I suggest that if Sir Alex is that concerned he should urge the FA to move their dates.”
The FA have held all semi-finals at Wembley since 2008.
And Ferguson for one is not impressed.
“It’s going to be absolute chaos,” he told Inside United.
“I don’t think the cost of people travelling down to Wembley is considered.
“There will be 60,000 people coming down from Manchester – think about how much petrol is used for that?”
The FA refused to comment directly on Ferguson’s remarks, although a spokesperson said they were “looking forward to welcoming all teams to Wembley” for the semi-finals.
The governing body also refused to comment on Bedford’s statement, instead pointing to the fact that everything has been agreed with the relevant authorities, such as transport links and police.