The campaign was won by the Oxford-based agency following a five-way pitch and will run for a year.
Sleep apnoea is the cessation of breathing while asleep, which can last for up to ten seconds at a time. In the most extreme cases, it can lead to no more than half an hour's sleep a night for sufferers.
ResMed, also based in Oxford, specialises in medications designed to treat sleep and respiratory problems.
Bottle's campaign will focus on three audiences: GPs, secondary care professionals including managers and nurses who work on specialist sleep treatment units within hospitals, and men aged over 40, who account for 60 per cent of diagnosed cases.
Sleep apnoea affects about one person in 100, but approximately 80 per cent of those who suffer from it are unaware of the condition and remain undiagnosed.
Emma Braithwaite, ResMed's UK head of marketing, said: 'Part of the strategy will be to look at how we can work alongside our secondary care customers to ensure they successfully maintain funding for what has been proven to be a cost-beneficial treatment.'
Bottle will work closely with GPs to highlight the condition and raise awareness of the symptoms and impact of sleep apnoea on work performance, personal relationships and health.
Carole Scott, director at Bottle PR, said: 'Before taking the brief, I had no idea what sleep apnoea was.
'But we have learned a lot in a very short time and we are determined that PR can make a difference.'