The phrase "a bid to run" is correct and usable in written English.
It can be used when referring to an attempt or effort to enter a race, competition, or position, often in a political context.
Example: "She announced a bid to run for mayor in the upcoming election."
Alternatives: "an attempt to run" or "a campaign to run".
Last year the toy company Bigjigs submitted a bid to run the west coast mainline.
His remarks were echoed by David Lammy, the Tottenham MP who is considering a bid to run as mayor of London for Labour in 2016, who said the remarks were worse than careless.
Bolivian voters appeared to have delivered a slim but stinging defeat to President Evo Morales after election officials announced he had lost a bid to run for a fourth straight term in office.
Sheraton, Hard Rock and a number of other companies competed for the project, and on Sunday it appeared that the Radisson hotel chain had won out with a bid to run the hotel as a joint venture.
Eurotunnel is to submit a bid to run the French ferry ports of Calais and Boulogne, the company has confirmed.
Greene competed at the trials in a bid to run himself into form after a torrid season so far.
He has much else to preoccupy him, not least an ongoing bid to run a new national television channel focused on local broadcasting, and his involvement in campaigning for the Alternative Vote.
For good measure, Mr. Martin, who made a failed bid to run on the Republican line in the 2004 race for a Senate seat from Illinois that Mr. Obama won, added, "We are basically going in the throes of a social revolution which attempts to essentially freeze out anybody who is not part of this radical ideology".
If the casinos, either individually or collectively, do make an aggressive bid to run the two tracks, it will mark a drastic turn of events for both industries in New Jersey.
McMullan made an unsuccessful bid to run for UKIP.
She divorced him at the end of his four-year term in an unsuccessful bid to run for president in 2011.
