Margot Parker said Mr Bolton should step down “sooner rather than later” because his “personal life took over the job he was elected to do”.
It comes a day after Ukip’s national executive committee (NEC) passed a vote of no confidence in their party leader.
The former army officer is facing widespread calls to quit amid an ongoing row over his personal life. He left his wife for 25-year-old glamour model Jo Marney but was forced to end what he called the “romantic element” of their relationship after it emerged Ms Marney had sent a series of racist text messages about the actress Meghan Markle, who is engaged to Prince Harry.
As the scandal rumbled on, Ukip’s NEC passed the vote of no confidence in Mr Bolton. He was the only member of the committee to vote against the motion.
Ms Parker accused Mr Bolton of leaving Ukip “in limbo”.
"It would be quicker and cleaner if he came to the conclusion he could go sooner rather than later,” she told BBC Radio Northampton.
"This is taking time away from doing the job. This puts the party in a limbo situation."
Ukip’s immigration spokesman, John Bickley, also resigned over Mr Bolton’s leadership.
“As the immigration and integration spokesman, I will be resigning today,” he told LBC. “I’m not going to do the job for Mr Bolton.
“I think it’s up to individual members and spokespeople and elected representatives, our MEPs and [assembly members] to decide they have to make it clear to Mr Bolton that his time is up and it would really be in his interest [to go].
“I believe he really needs to go and focus on sorting out his personal life and get away from politics.”
Another frontbencher, trade spokesman William Dartmouth MEP, also quit on Monday.
He told his party leader: "Your position is untenable. I am unable to serve under you.
"Your personal life has become the entire story...When you became leader you said that you would make the party successful. If you still feel that way then you should resign forthwith."
Despite the backlash, Mr Bolton insisted he would carry on as leader.
“I don't believe I have done anything wrong,” he said on Sunday.
"My own personal life, it's a little bit of a mess at the moment. I need to sort that out, of course."
He will now face a vote of party members at an emergency meeting to determine whether he should continue in the role.