Airport Extreme Basestation as airprint

I have an HP printer connected to an Airport Extreme Basesation (N support only, ac was not available at that time. Originally, it was connected to a Windows PC (mother's PC) and it would not work as a network printer with other than Windows. Then I connected the printer directly to the Airport Extereme Basestation. I worked perfectly (although had to add in Bonjour to Windows PCs) for everything, our iPads, our iPhones but most importatnly all the Windows PCs and Macs. Then my mother's PC died. So, I got my mother a MacBook Air, as she wanted a laptop instead of a desktop and was intrigued by the Mac as I had been using Macs for decades. Well, everything except my mother's MacBook Air can print to that HP printer connected to the Airport Extreme Basestation. This has me a bit flumoxed since everything else, including her iPad can print to the effeictive Aiprinter, except my mother's Mac. Until the death of my mother's Windows PC, I was able to install Bonjour and was able to print from the PC.

I went to tha Apple Store, the night of my mother's PC's death and all they had was the i5 8GB RAM, and 256 SSD, but i figured it was enough for her.

For some reason, maybe previous stock, it came with Mountain Lion, but the salesperson said so, so it wasn't a surprise. After the initial setup, the first thing I did was to install Mavericks. I have a MacBook Air, but I opted for the larger SSD and full 8GB memory and i7 CPU, it too came with Mountain Lion, but I bought ti before Mavericks. First I had a backup of my mother's Outlook file on a flash drive, and I also have a Office 365 license so I installed Office including Outlook (since she had been using it for years under Windows, and she was most familiar with that) I installed one of my licenses, and everything was/is working fine, until it came to printing. So, I was able to recover everything she needed except printing.

Does anyone know what needs to be done to get Airprint working? I can see it from the Mac, but it won't print. If I direct connec the printer to the Mac, it works fine, but then the rest of the divices won't be able to print unless her Mac is not only powered on, it has to be logged in to where the printer is shared. That works, but now that my mother has a Laptop, she takes it with her. I also have an HP printer connected to my Mac and its printer is shared, however, I take my Mac to work. This leaves the rest of the family wihout printing unless my mother or I have our Macs connected, powered on and logged in. I want to put the printer back on the Airport Extreme Basestation. Any suggestions? I see some Airprint Activator software, but there should be no reason to need it.

Thanks for any one who can help.