The company, whose suits and kilts can be hired through high street chains Burton, Austin Reed, Slaters and Greenwoods, will use the funds to expand Xedo, its bespoke software division.
It plans to put the final touches to the e-commerce platform it began to build when it moved to its 190,000 square foot premises at Lanarkshire's Eurocentral business park in 2012.
The latest investment means ACS is on course to offer a multi-channel service to its retail partners, allowing consumers to hire formal outfits through its customers' discrete websites.
One facility, sortmyweddingoutfit, is designed to meet the clothing needs of wedding party members, regardless of location.
Richard Freedman, who established ACS with his father Joseph in 1997, has flagged investment in e-commerce and software processing as offering the "quickest way to expand our business".
And he noted the benefits the BGF backing has brought versus the longer process involved in securing traditional debt finance, particularly as "IT moves so quickly".
Xedo already supplies software products to the hire and wedding industries, including a retail order management system that connects ACS Clothing and Xedo customers direct to its inventory. This allows hirewear to be ordered electronically.
Mr Freedman, who has no plans to add to the firm's solitary store, Gilt-Edged, in Glasgow's Saltmarket, highlighted the growing importance of e-commerce to retail businesses.
He said: "The retailers that are doing best are the ones with the strongest online and multi-channel offering.That's really why the investment we have got with BGF is to make sure that our business is ready in a few years for where retail is going."
He added: "The argument has moved away from whether to do multi-channel, to how."
In addition to the IT investment, he said the company plans to "reinvigorate" its stock, as well as take steps to expand overseas.
It has received an additional £3m of finance from Clydesdale Bank, which, along with Lombard, had helped fund the fit out of its Eurocentral premises.
ACS holds more than three million garments at the facility, having processed 400,000 UK orders last year. It utilises an automated stock control and garment sorting system which is able to process 5000 items simultaneously.
The wedding season marks the peak period for the business, which turns over £11.5m and employs about 100 staff.
While Mr Freedman described 2013 as a "terrible year" for weddings because of superstitions over the number, he said "2014 is shaping up to be a very strong year for us".
He added: "We do feel there is more confidence about in general. I think you can put off a wedding for a year or two - after that you kind of get round to it."
BGF has taken a minority stake in both ACS Clothing and Xedo as part of the deal, with its regional director for Scotland, Simon Munro, joining both boards.
The boards will also be augmented by a new external chairman as soon as he or she is recruited.
The investment in ACS Clothing is the ninth BGF has made in Scotland since being set up by five major banks - Barclays, HSBC, Lloyds, Bank of Scotland and Standard Chartered - to help grow businesses that turn over between £5m and £100m.
Mr Munro said: "Richard is an extremely talented entrepreneur and I am very excited that BGF will have the opportunity to invest in his business during a crucial time of growth.
"Our team has not only been impressed with ACS's hi-tech and efficient operations but also with the scale of the business opportunity.
"Formal hirewear has huge market potential, both in the UK and internationally, which means that we have a number of exciting opportunities to review."