Office for National Statistics (ONS) data shows 6,985 people in the area were claiming out-of-work benefits as of mid-May, down from 7,355 in April.
It means 6.6 per cent of Bedford's working-age population sought support in May – down from 6.9 per cent the previous month.
And it was also 335 fewer than the number of claimants recorded in May last year.
The figures include those aged 16 to 64 on Jobseeker’s Allowance and some Universal Credit claimants, who are unemployed and seeking work or employed but with low earnings.
The ONS cautioned that changes to Universal Credit in response to the virus mean more people can get the benefits while still being employed, which could affect the figures.
It also said a small number of people who can claim both JSA and UC could be counted twice.
National figures, which are adjusted to account for seasonal changes, show the number of people seeking help across the UK fell by 92,600 month on month to 2.5 million in May.
This period covers the reopening of outdoor hospitality and non-essential retail for the first time since December.
The ONS said the number of payrolled employees jumped by almost 200,000 in May – a record monthly rise – but remains more than half a million below pre-pandemic levels.
Sam Beckett, ONS head of economic statistics, said: “Job vacancies continued to recover in the spring, and our early estimates suggest that, by May, the total had surpassed its pre-pandemic level, with strong growth in sectors such as hospitality.
"Meanwhile the redundancy rate remains subdued, while the number of employees on furlough has continued to decline."
Stephen Evans, chief executive of Learning and Work Institute, said the figures show the labour market is recovering as the economy reopens – but the crisis is by no means over.
He added: "Repairing the damage is likely to take years with long-term unemployment already up 50 per cent% compared to last year.
"The furlough scheme limited the worst of the damage; employment support needs to make the most of the recovery."
Across the UK, 143,000 men came off unemployment benefits between May 2020 and last month – almost 10 times more than number of women.
In Bedford, 335 fewer men were receiving support over this time, compared to five more women.
Chancellor of the Exchequer Rishi Sunak said: “Our Plan for Jobs is working – the latest forecasts for unemployment are around half of what was previously feared and the number of employees on payroll is at its highest level since April last year.
“We understand the value of work and the distress caused by unemployment – that is why we are continuing to support people and jobs."