Unfortunately, you cannot use Keynote Remote via Bluetooth with a Mac. However, as an alternative to the spotty wifi, you may consider creating your own 'computer-to-computer' WiFi network from your MacBook Air.
When a Wi-Fi connection is unavailable you can use Keynote Remote with Bluetooth to control your Keynote slideshow from one iOS device to another (iPad, iPhone, iPod touch). However, slides may take longer to appear on Keynote Remote when connected via Bluetooth. You cannot use Keynote Remote via Bluetooth with a Mac.
All the best,