The company also reported positive cash flow for the month after it started reopening stores to the public in late May. It said that as of last week, nearly all of its stores were back open.
Shares were rising 3.4% to $7.99 on Tuesday morning.
Total net sales were only down 7% year over year for the month of June, thanks in part to an 80% increase in digital channel sales versus a roughly 25% decline in physical sales.
The company also announced that it is accelerating its cost restructuring program and intends to improve EBITDA by between $250 million and $350 million this year.
The company said it will accelerate plans to reduce its store count by 200 over the next two years, saving about $100 million annually in the process. The retailer also expects to save another $200 million a year by renegotiating product sourcing with existing vendors.
The company previously announced that it was planning to aggressively reduce up to $1 billion of inventory; as of the fiscal first quarter ending May 30, Bed Bath & Beyond said that reduction plan is "slightly more than halfway complete."
Earlier this month, Bed Bath & Beyond reported fiscal first quarter results that missed expectations and shares plunged in response.
"We're going to come into the post-Covid period as a very fresh company," said CEO Mark Tritton, who took over the company in November, during a conference call with analysts.
That effort includes Buy Online-Pick Up in Store, as well as "a whole new set of customers and a new way of working in an omnichannel way."
In an interview with CNBC following its fiscal first-quarter earnings release, Tritton said the company's previously announced review of its noncore assets is a "work in progress."
But he added that he sees its Buy Buy Baby chain as a part of the company's core plans moving forward.