The Typekit Services Agreement does not permit fonts synced from Typekit to be transferred to another user or computer that isn't already licensed for that font.
The "Packaging files that use synced fonts" help page has more information on this: http://help.typekit.com/customer/portal/articles/1166052
For now, you can export a PDF and send this to the printer, or the print bureau can easily use the same fonts if they have a Typekit account or full Creative Cloud subscription.
I'm sorry I couldn't be of more help here. Let me know if you have any further questions.
you cannot force printers to move to typekit....
… And that is exactly why for modern print workflows, we most strongly advocate production of PDF (and preferably PFD/X-4) files with fonts embedded from which your printers produce printed output in lieu of sending them source files including placed imagery and fonts.
… "For font software licensed from Adobe, your license agreement provides that you may take a copy of the font(s) you have used for a particular file to a commercial printer or other service provider, and the provider may use the font(s) to process your file..."
You are quoting only part of Adobe's EULA (End User License Agreement). Yes, you can provide a copy of a font you licensed from Adobe with source files in which you use such a font to a printer, but only if the printer has licensed the font as well. There is no “free use” of fonts for printers, even if many print service providers blatantly violate these rules and request fonts that they have no license for from customers.
The best solution to this is for customers to submit print ready PDF/X-4 files (with fonts embedded) to their print service providers. This solution is totally compatible with Typekit!