Jo Swinson is running for the Liberal Democrat leadership, and if the bookmakers are right, she is on course to win: but she’s not enjoying it very much.

“There is something that is inherently a bit more uncomfortable being up against somebody [her leadership rival Ed Davey] who’s on your team, who you get on with, and who you’re going to be really close colleagues with, whatever the outcome,” she tells me on a train journey to Bournemouth, where she is speaking at a local government conference in her role as the party’s deputy leader.

Swinson was selected as the Lib Dem candidate in East Dunbartonshire in Scotland –where she grew up and went to school – in 2005, and has been the party’s candidate there ever since. Her first reaction on being elected to parliament, overturning a Labour majority, was, “Thank God, I don’t have to do any more selections.”

“In the Tories and Labour, you are at least talking about massive broad churches – where you’ve got Liz Kendall and John McDonnell, obviously, there’s going to be some broader policy differences. In a party like the Lib Dems, where we’re very united, it feels a bit more like, ‘I think I’m better than him’ – and I do, but it doesn’t necessarily feel so kind to stand up there and say that about a colleague, right?”

That challenge is perhaps more acute for Swinson, who has been a Lib Dem since secondary school. “Two issues drew me to the Liberal Democrats: education and PR,” she says. On the one hand, local schools were groaning under the weight of spending restraints, while on the other, the electoral system made voting feel pointless “because if you voted Labour they were going to win anyway, and if you voted for anyone else, then your vote didn’t count”.

She was impressed by Paddy Ashdown, the party’s then leader, and his commitment to raising taxes to pay for more education spending – and she formally joined at university. “I knew I was a Lib Dem, and I was joining everything else. I was joining the Flamenco Society, and who knows what else, so yes, I paid my whatever it was, two pounds, and joined.”

Time in the Liberal Democrat Society led to an invite to a residential training weekend. “Basically, the reason I went was partly because I’d planned to go to Paris with my boyfriend and we’d split up, and I was kind of mooching about,” she recalls. “So this invite came in, and I thought, it was only a tenner, I’ll just go to this, meet some new people, what’s the worst that can happen?”

The “worst” turned out to be election to the party’s national executive and, eventually, a return to her home town, winning the seat from Labour with a majority of a little over 4,000. First as a backbencher and then as the party’s shadow Scottish secretary, she made a name for herself as a campaigner – presenting a bill to parliament for the reduction of excessive packaging, and leading a campaign on body confidence.

In coalition, she was parliamentary private secretary, first to Vince Cable and then to Nick Clegg, before finally becoming a junior minister in the business department. She describes her promotion from being Cable’s PPS to Clegg’s as a “surreal event”. Chris Huhne had been forced to resign from government and Clegg was conducting a reshuffle during a party away day in a hotel in Eastbourne.

“He knows that I do a lot of campaigning as well, and he said, ‘You know, I don’t want you to feel you have to stop that, you can still keep doing your Bodyform stuff.’ And I said, ‘Nick, you know it’s not Bodyform, right?’”

“Well, whatever it is.”

“It’s body image: Bodyform’s a brand of sanitary towels.”

Despite her political proximity to Clegg, Swinson was never promoted to the cabinet. Nor were any Liberal Democrat women during the life of the coalition. I ask her if she thinks that Clegg’s inability to remember what her feminist campaigning was about, and his failure to promote a single woman to the cabinet, are linked.

“I don’t know,” she says. “It’s not intentional, but we still operate within a society where there are levels of unconscious bias and assumptions that are constant, that are almost imperceptible, but they kind of layer on, and they shape the politics that we have.”

That belief has led her to abandon the usual safety-first playbook of a front-runner, repeatedly challenging her party’s record on racial and sexual diversity.

“I recognise I’m hugely privileged, but I think a lot of people within the political system do not clock how much that is the case, and I think that’s why I’m a bit challenging sometimes with the party.”

One of the challenges Swinson has made to her party is to “own the failures” of its time in coalition. “Not in a sort of beat-yourself-up-about it-constantly way, but just in a matter of fact way: there were some amazing things that we did and we rightly talk about them, and if we try to pretend that we didn’t get anything wrong, then people won’t believe us about the things that were great.”

Will that be one challenge too many for the Liberal Democrat grass roots? Whatever happens, Swinson isn’t going to let that compromise her campaign, even if she will be relieved when it’s all over.