Murray last week increased his stake for the third time since September, buying 7,482 shares at 277p each following earlier purchases totalling 17,500.
He now holds more than 101,000 shares in the firm, which has seen shares rise by 14 per cent in the past fortnight.
Several other directors have also been upping their stakes in recent months.
In November, BSS reported a drop in interim profits but said current trading performance was in line with expectations.
• John Aldersey-Williams, a non-executive director at Aberdeen-based offshore wind developer SeaEnergy, has increased his holding. He bought 20,000 shares at 57p each and now holds 67,816.
• Dr John Brown, a non-executive director at Dundee-based medical diagnostics group Axis-Shield, has bought his first stake in the company with 7,500 shares at 410p each.
Iain McLaren, a non-executive director of the Baillie Gifford Shin Nippon trust, has bought his first stake in the Japan-focused investment vehicle. He purchased 10,000 shares at 117.89p.
• Three directors at drug group Sinclair Pharma have increased their stakes as part of an 18 million fundraising.
Chief executive Chris Spooner, chairman Grahame Cook and non-executive director Jean-Charles Tschudin invested a total of more than 900,000 in shares at 32p each.
The fundraising is to finance the purchase of two products from Solvay.
• Susan Taylor, a non-executive director at Renovo Group, has bought her first stake in the biopharmaceuticals group. She bought 20,788 shares at 28p.
• Jeremy Dowler, non-executive chairman at Baobab Resources, has upped his stake in the company for the second time in a fortnight.
He purchased 550,000 shares at around 7p a share last week after buying 100,000 at 4.65p in December. He now holds 7.89 million shares in the Mozambique-focused iron ore, base and precious metal explorer.
• Andrew Varley, group property director for retailer Next, has reduced his stake. He sold 8,879 shares at around 20.60 but still holds just over 61,000 shares in the group.