Ok, so it turns out a comment regarding VSO on the same link I provided also works for BitBucket, I've included the comment here for reference...
A fix for this issue should come soon, for now as a temporary workaround:
Create a "webjobs.props" file and add it to your Properties
folder in whichever project you want to publish from. (Both WebJob and WAP if you want to publish from either)
<Project xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
<PropertyGroup>
<CopyAllFilesToSingleFolderForPackageDependsOn>
$(CopyAllFilesToSingleFolderForPackageDependsOn);
AddWebJobFilesToPublish;
</CopyAllFilesToSingleFolderForPackageDependsOn>
<_DestinationType>AzureWebSite</_DestinationType>
</PropertyGroup>
</Project>
Comment provided by amitpal @ https://gist.github.com/amitapl/ff51f6ecc7cc052ef0f7