Bick, who has been at Holborn for five years, joined Regan's bid vehicle Corvus Capital last Thursday as its first head of communications. Bick will also act as spokesman for Regan, who is chief executive of Corvus.
The move comes less than three weeks after Corvus abandoned a £2.4bn bid for FTSE 100 insurer and More Than brand owner Royal & SunAlliance.
Corvus had no direct contact with RSA, which learned about the planned bid through the media and declined to co-operate.
Although the company is now barred from making another bid for RSA for at least five months, it is reportedly scouring five industry sectors for acquisitions and is particularly interested in financial services.
The collapse of the RSA bid was a blow for Regan, who hoped the deal would help him return to the centre of City life following his controversial 1997 attempt to buy mutual group Co-operative Wholesale Society. In 2003 Regan was cleared of fraud charges related to the £1.2bn Co-op approach.
Bick, who handled Holborn's account with Corvus, said there would be no review of Corvus's comms in the short term.
'There are challenges,' he told PRWeek. 'But the expertise of our management team means that we are capable of meeting those challenges.'
While at Holborn, Bick worked on communications around several high-profile transactions, including WalMart's 1999 acquisition of supermarket Asda.
Prior to joining Holborn, where his older brother David is chief executive, Bick was an equity partner at Financial Dynamics.