HDD? I must admit that I have never tried that myself. It makes sense it will work being either HDD or USB drive (pen-drive). Boot Camp makes whole thing automatic so you do not need to think about partitions, formatting, drivers. It does all that...well, it should. The only thing that I have encountered that booting from USB 3 compatible drive (either HDD or flash drive) can be hit or miss with MBA. However, USB 2 (only) devices seem to working just fine.
It won't solve your issue, but did you/can you try booting from flash drive on another machine (PC/Mac)? Just to rule out non-bootable issue with drives themselves.
Another option - instead of creating bootable drive via Boot Camp, try creating one using a Windows machine with this tool:
http://www.microsoftstore.com/store/msusa/html/pbPage.Help_Win7_usbdvd_dwnTool
It is pretty straightforward, choose ISO location, insert a drive and let it do the rest.
Alternative is to use Remote Disk if you have another computer with DVD drive.
http://support.apple.com/kb/HT5287?viewlocale=en_US&locale=en_US
I realise that you might not have a second computer to try any of these but I cannot think of any way to resolve this besides verifying that created installation disk is indeed bootable (another computer). Trying to re-create disk via Boot Camp or Windows USB tool without manually formatting/creating partitions on destination drive.
Stupid question, but if you used HDD to do the installation, did you create partition table/partitions manually first? It could be MBR/GPT issue. Use a drive which you can fully erase and use for installation.
Edit: It would be best if you could provide more details machine model/year, OS version, type of HDD/pen drives you are using... Perhaps someone who has the same model could be of a more assistance. Maybe there is a workaround of which I am not aware of. Apple recently issued EFI updates for 2013 models which could help if you did not apply the updates, for example.