The incident happened during a refurbishment project at offices in Sentinel House, Poole over a period of several weeks in 2009.
Bournemouth Crown Court heard that MJC Decorating and Refurbishing Ltd began removing ceilings at the two-story block without carrying out a suitable asbestos survey.
An HSE vist revealed widespread contamination and spread of asbestos both inside and outside the building.
Material removed from the site as non-hazardous may have included asbestos-containing materials.
As a result, four employees and 14 agency staff working under the control of MJC, were exposed to asbestos dust and fibres.
MJC workers carried out the removal of asbestos insulation board ceiling over two weeks while wearing normal work clothes that became contaminated with asbestos fibres.
This may have led to the exposure of many more members of the public during their journey to and from the site over this two week period.
MJC Decorating and Refurbishing Ltd, of Sutton, Surrey, pleaded guilty to three safety breaches and was fined a total of £45,000 and ordered to pay £36,943 in costs.
Speaking after the hearing, HSE Inspector, Helena Tinton, said: “This was a very serious incident which carries severe risks for people’s health.
“MJC’s safety failings led to the needless exposure to dangerous asbestos fibres of its employees, agency staff and the wider public.
“The firm didn’t carry out a suitable survey for asbestos material before the work started and failed to provide protection for workers on site.
“Regulations on dealing safely with asbestos have been in place for many years and are widely known in the industry.
“This totally needless incident would not have happened if MJC had carried out proper assessments and had trained staff on site.”