Houston Mayor Annise Parker and D.C. Council member and mayoral candidate Muriel Bowser. Bowser has traveled to Houston and other cities in recent months. (Muriel Bowser mayoral campaign)

Since winning the Democratic nomination for D.C. mayor in April, Muriel Bowser has sought to avoid the brickbats of an unusually close-fought general election race. To help rise above the fray, the D.C. Council member has been traveling around the continent to gain experience as a potential mayor while adding to her campaign coffers.

In the past two months, Bowser has visited mayors in Houston, Atlanta and Montreal, supplementing trips made earlier in her campaign to Pittsburgh, the San Francisco Bay area and Austin. Trips to Philadelphia and New York are in the works.

Bowser, in an interview Thursday, said the trips have broadened her political and policy horizons, introducing her to “best practices” elsewhere and some of the nation’s most effective public officials.

“We’ve just worked into the schedule getting out to other cities to see what’s working in those cities and what’s not and find out from them what can be done here,” she said. “It has been very instructive.”

Also, in some cases, lucrative: The trips to Atlanta, Houston and the Bay Area included fundraisers, campaign spokesman Joaquin McPeek said Friday, helping the candidate to pad a million-dollar war chest.

The travel, however, has come amid criticism that she has been unwilling to engage in debates with fellow candidates back home, and it has opened her up to accusations that she has been neglectful of her duties in the District, where she represents Ward 4.

In Houston last month, Bowser met with Mayor Annise Parker (D), with whom she said she discussed the approach that the nation’s fourth-largest city has taken toward affordable housing, homelessness and infrastructure financing. “What’s innovative is that they’ve laid out a long-term plan,” Bowser said. “We’re going to have to have that kind of plan.”

This month, Bowser visited with Montreal Mayor Denis Coderre while on a trip organized by the Institut du Nouveau Monde , a nonpartisan democracy-building group in Quebec. Those discussions, she said, focused on Coderre’s approach to his first 100 days in office, as well as his focus on creating a “smart and digital city.”

Bowser was most recently in Atlanta, where she met with Mayor Kasim Reed (D) and his deputies and received briefings on the city’s plans to build a football stadium and the impending opening of its first streetcar line . Most instructive, she said, was meeting with members of Reed’s Office of Innovation Delivery and Performance .

The operation has much in common with data-driven accountability regimes such as the District’s former CapStat and Baltimore’s long-standing CitiStat programs, but Bowser said she was impressed by Atlanta’s operation.

“They are working on the next iteration of performance evaluation,” she said. “They’re not only measuring but soliciting more information. . . . For them, it’s about collaboration between the city management level and the agency level, but for me, I would have another twist on that, and that is how to have more real-time communication with the public.”

Bowser’s whirlwind tour is reminiscent of former mayor Adrian M. Fenty’s. Before taking office in 2007, he visited leaders in New York, Chicago, Los Angeles and Baltimore — big-city mayors whom he considered his peers — pressing them for insights on how to improve governance.

In perhaps his most famous field trip, Fenty dragged most of the D.C. Council and a pack of reporters onto an Acela Express train to New York as he floated the idea of disbanding the District’s Board of Education and taking direct control of D.C. Public Schools. The trip helped build support among lawmakers for the school-takeover plan, but what critics saw as Fenty’s seeming obsession with acting like an imperious “big-city mayor” would later alienate allies and doom his political prospects.

Bowser said she is undertaking her explorations “quietly and effectively” and played down comparisons to Fenty’s travels. “I’m just gathering information to help me inform my thinking in how we organize the city,” she said.

Her most aggressive rival in the mayoral race has taken notice. After Bowser tweeted a picture of herself with Coderre, independent candidate David A. Catania’s campaign threw together a mock postcard reading “Bonjour Muriel,” criticizing her for leaving town while a controversy over her handling of the troubled Park Southern Apartments metastasized.

“No one has a problem with it if she were doing her job here,” said Ben Young, campaign manager for Catania, an at-large member of the D.C. Council. “While she’s been globetrotting, David’s been in the living rooms of D.C. residents talking about substance and policy.”

Bowser said Thursday that the criticism is misplaced. “I think that a mayor of a major city like Washington has to focus on all the matters at hand in the city and also prepare the city to be a regional, national and global competitor. You do that by learning what’s working in other places.”