The headline index figure in January hit 57.2, which was up sharply from the 54.5 recorded in the final month of 2013.
The pace of expansion was still slightly slower, however, than that observed across the UK as a whole, says the bank.
Donald MacRae, chief economist at Bank of Scotland, said: "The growth in new export orders after two months of decline is particularly welcome.
"Business confidence continues to increase, ensuring the Scottish economy not only continues the recovery but enters 2014 with growth momentum."
In the service sector, business activity accelerated in January at its fastest rate in three months. Firms reported increased confidence among clients and an associated rise in incoming new work.
January's expansion was the thirty-seventh in successive months and broad-based, though it was led by financial services.
The service workforce expanded, albeit modestly, for a twentieth straight month, on the back of increased workloads. Some firms expect further recruitment to meet demand in the coming months.
Services firms also recorded a faster increase in new business wins in January, regaining the ground lost in December, and the growth rate was among the highest on record.
"Financial services firms posted the most marked rise in new business, followed by those operating in business services and then travel, tourism and leisure," the bank said.
Backlogs of work increased again, and the rate of input price inflation in Scotland's service sector eased after hitting a nine-month high at the end of 2013, with tourism and leisure again seeing the steepest rises in operating costs from across the industries.
Nearly 11% of survey respondents recorded a rise in their average tariffs, compared with 6% posting a decrease.
January also saw a return to strong growth in Scottish manufacturing output after a loss of momentum in the final quarter of 2013.
"The seasonally adjusted index was the second-highest in nearly three years, just slightly below its level in July 2013," the bank said. Production levels had now increased in nine of the past 10 months.
Scottish manufacturers also stepped up their rate of job creation, which was the fastest rise since last July, the twelfth in a row, and among the sharpest in the series' history.
Intakes of new work at Scottish manufacturers increased again in January, stretching the current sequence to 13 months.
"The rate of growth in new orders was sharp and the fastest since last August's survey near-record," the bank said.
"Anecdotal evidence pointed to an increase in demand, from both domestic and overseas markets."
New export orders rose for the first time in three months."
Although only modest, the increase in overseas sales nevertheless represented a marked turnaround from the marked rate of contraction registered in the preceding survey period, the bank said.
"China was highlighted by panel member reports as a source of new business wins."
The level of purchasing activity among manufacturers north of the border returned to growth in January, while backlog depletion was the weakest since August, and inventories remained strong.
Operating costs however rose at their fastest for ten months, driven by higher raw material prices, feeding into a 25-month high in output price inflation.