Bowie, owner of haulage and waste disposal firm Billy Bowie Special Projects Ltd, had invested £250,000 earlier this season to become the second largest shareholder.
Johnston, who did not attend last night's open meeting held by the supporters association, also said talks were ongoing with Supporters Direct with a view to "community involvement" in a proposed new board.
"I apologise for my absence from your meeting this evening, due to a prior engagement," wrote Johnston on the official website. "I hope you have a constructive discussion which results in a consensus to put aside recent acrimony and revert to the Association's sole objective of promoting the support of Kilmarnock Football Club.
"I'm pleased to report that a further meeting took place yesterday at Rugby Park with Paul Goodwin of Supporters Direct. Billy Bowie and I reiterated to Paul our desire to promote community involvement in the new Board of Directors of the football club, which we intend to form following the implementation of our financial restructuring plan. Our shared vision is to have an open and transparent process for the election of a Director by season ticket holders and another Director by shareholders holding under 1000 shares in the Club. East Ayrshire Council would be invited to nominate a Director and the Members of the Scottish and UK Parliaments representing Kilmarnock would be invited to join the Board. We have invited Supporters Direct to investigate the creation of a working party which would embrace all supporters groups, along with local business leaders and politicians with a view to engaging in a constructive dialogue."
Johnston praised Bowie for his investment. He said: "I'm delighted to report that Billy Bowie Special Projects Ltd has committed to investing a further £1m in the Club to assist in the financial restructuring project which I have been working on for over a year with the full support of Lloyds Banking Group."