Several said it would mean the difference between opening or not, and "wholeheartedly" welcomed the proposal.
Currently businesses must operate under a two-metre rule, but this may be reduced to 1m - with safeguards.
Customers can sit in restaurants and bars in Scotland from 15 July.
The Scottish government said it would set out guidance at the end of next week on how the the industry could operate.
However, it said "for illustrative purposes and to allow businesses to start to plan" it would give some guidance in "general terms" including plans to let businesses decide to operate at less than 2m as long as they had a warning in their windows.
Tom Ponton, owner of the Oz Bar in Edinburgh's Grassmarket, said he "wholeheartedly" welcomed the idea.
He said: "This is the difference between me opening and not opening.
"It is the best news for the entertainment industry so far.
"Even at 1m we are going to have to cut the capacity but at 2m it is impossible."
Billy Lowe, who owns The Black Ivy in Bruntsfield and McSorley's in Edinburgh's city centre Forrest Road, said he would put a sign up in his window straight away if the government went ahead with the plan.
He said: "We had been considering not opening because the two-metre rule wouldn't allow us to get the numbers to make it viable.
"So this news is a game changer.
"I also love the sound of the sign because then people know what they are getting when they enter and can't complain.
"I had foreseen conflict between customers with the two-metre rule but if there is a 1m sign outside in the window then that will stop all that."
Daniela Scott, who runs her father's Italian restaurant Gordon's Trattoria on Edinburgh's Royal Mile said she was very relieved the government was now considering the one metre rule.
She said: "This is a game changer in the restaurant trade and makes me feel like we have a bit more of a chance of survival.
"I 100% welcome putting a sign up in the window.
"The one-metre rule means we could have another 10 seats in the restaurant. The thought of it makes me feel relieved."
Mohammed Parvez, 55, owner of the 42-seat Indian restaurant Rannaghor in Edinburgh's Currie area, said he welcomed the news.
He said: "This is what the customers want. They have been calling me asking when they can sit in the restaurant and said they don't want to sit 2m apart.
"Eating in a restaurant is all about the buzz and atmosphere of being out with others and enjoying lovely food, they don't want to be sitting in a sparsely filled place.
"I absolutely welcome this latest development and urge the Scottish government to follow through with this plan."
Steven Hall, general manger of The Dome in Edinburgh said: "This is a step in the right direction. I would welcome it but we also need to see what the other guidance and regulations will be."
The Scottish government said in its briefing on Thursday: "For illustrative purposes and to allow businesses to start to plan, we are publishing today the kinds of mitigations that might be required in each sector.
"However in general terms, these might include improved ventilation; Perspex screens; regulation of customer flow and seating plans that reduce transmission risk.
"For hospitality and possibly others, mitigation will also include the collection of names and addresses of customers, to help with contact tracing when that is necessary.
"And we will also insist on clear customer information to help inform the judgments we all make as individuals about the risks we are prepared to take.
"So if a business decides to operate at less than 2m, they should provide clear signage informing their customers that they are entering a one-metre zone.
"We hope to have guidance agreed for the start of phase 3 and ahead of the opening of tourism and hospitality from 15 July."
The question isn’t who is going to let me; it’s who is going to stop me.