INDIANAPOLIS—Across the country, voters this year are expressing disdain for Washington and the political operatives who work there. But in Indiana, that may not apply to Evan Bayh.

Donald Trump’s derision of longtime politicians may have helped him secure the GOP presidential nomination, and Bernie Sanders’s outsider appeal gave him unexpected strength in the Democratic contest. But Mr. Bayh, the Democratic candidate for Indiana’s open Senate seat, appears to be helped by his political lineage and years of experience. A...