There is no Desktop (AIR) version of Adobe Send. You can send through Adobe Reader, Microsoft Outlook (Windows) or the web client (cloud.acrobat.com/send).
I opened an Adobe PDF document in my MacBook Pro and the Adobe Send option opened up, giving me no information that I couldn't send it as it was entered into their "send" box. I just subscribed and now you're saying I can't go back to the site from which I subscribed and send the document...is that correct?
Sorry if my response was confusing. We don't have a *desktop* version of Adobe Send, as we did with SendNow, a similar service that is being retired later this year. That's what I thought you were asking.
You can use the Adobe Send service in Adobe Reader as well as from the web client (just go to https://cloud.acrobat.com/send and sign in with your Adobe ID and password). From your description, it sounds as though you had opened the PDF document in Adobe Reader. If you want to send from Reader, open the PDF file again, then select Send Files from the panel on the right. If you don't see it, click on Tools. You'll need to sign in, as well.