The bank’s monthly purchase managers index (PMI) recorded the strongest economic performance since January last month.
The service sector was the primary driver of growth, as a solid increase in new business drove activity up for the second month in a row.
There were reports of success in winning new business from both domestic and international clients.
But output in the manufacturing sector was reported to have fallen for a second month running due to a lack of incoming new orders.
General election uncertainty and difficulties in sourcing new export business were reported to have weighed on new work.
Latest data showed that employment rose for a fourth month in a row.
With manufacturers indicating little change in their payroll numbers, growth emanated mainly from service sector companies.
Panellists reported that staff had been taken on in response to higher workloads.
Both sectors recorded declines in work outstanding during May. Manufacturers blamed a lack of new business and the completion of large jobs as reasons for the latest cut in backlogs.
Higher supplier charges and an uptick in average salaries pushed costs higher in the services economy.
Donald MacRae, chief economist at Bank of Scotland, said: “May’s PMI at 51.9 was the highest for five months driven by robust growth in service sector activity.
“Although manufacturing output shrank, the rate of decline slowed.
“Employment and new business increased across all sectors.
“New export orders for manufactured goods declined but at a reduced rate compared to last month.
“The Scottish economy is regaining some growth momentum lost in January this year.”