Employment levels were up for the fourth month in a row while the number of job vacancies also accelerated, according to the bank's latest labour market barometer.
However, jobs growth in Scotland continued to lag behind the UK average, while rising numbers of Scottish jobseekers also subdued rises in pay rates.
The Bank of Scotland labour market index hit 54.2 in March, where 50 marks no change on the previous month. This compared to the UK index which measured 56.5 – although the UK showed a slight decrease last month.
Donald MacRae, chief economist at the bank, said the "reassuring" figures showed the Scottish economy was "recovering from recession".
The bank's index is a composite indicator which measures demand for staff, employment, the number of jobseekers and pay in the permanent and temporary job markets.
The data is collected in a monthly survey of more than 100 recruitment and employment consultants by research firm Markit.
The survey revealed vacancies in most sectors of the economy, although IT and computing workers were in the highest demand among employers searching for both permanent and temporary staff. Both permanent and temporary placements rose in March, although growth was driven by demand for temps, which accelerated at the fastest rate since August 2007.
The number of staff placed in permanent jobs also grew sharply in March, albeit growth slowed for the third consecutive month.
Recruitment agencies in Edinburgh registered the strongest rises in both permanent and temporary placements, which in turn drove up pay rates. In the same month, Glasgow had the sharpest rises in the number of workers available.
As a result of the rise in available workers across Scotland, pay inflation in March was "mild" and weaker than seen in February. Hourly pay for temps rose at the fastest since August 2007.
The survey is published just days before the latest Scottish GDP figures for the fourth quarter of 2009.
Economists warned at the weekend that it is "touch and go" whether the figures will reveal that Scotland officially exited recession during the period despite an improvement in certain areas of the economy.
A string of leading economists told The Scotsman's sister paper, Scotland on Sunday, that it may take another three months before an end to the recession north of the Border can officially be declared, even though the UK economy as a whole recorded 0.4 per growth during the closing three months of 2009.