I've sold and shipped numerous bikes from Canada to other Canadian addresses and to the US. I've never had a problem. I used Paypal for the US transactions and Interac through my bank [TD] for Canadian transactions.
For shipping in Canada I'll use Canada Post for a frame since I can get the size of the box down to legal dimensions...won't work for a full bike. For a whole bike in Canada Greyhound has been good for lower costs.
To the US I'll use Canada Post/USPS for frames and if I need to ship a complete bike UPS/FEDEX. Taxes and duties are the buyer's responsibility on the receiving end. There is no practical way to deal with that in advance. I have received bikes from the US via DHL, but never shipped that way. My work gets 25%+ off FEDEX shipments due to our volume and they don't mind if I use the company account for personal stuff and just pay them back.
Most LBS will give you free bike boxes. When I have had to ship oddball sizes like recumbents [don't judge!] or really large frames like touring bikes I just got two normal sized boxes and cut up the second one to act as an extender for the first one. The box size will directly impact shipping costs so the more you can take the bike apart and pack in a smaller volume the better. Each shipper will have a maximum size they'll ship so check on that and plan out how big your box can be in advance.
I like pipe insulation for packing a bike. It's low cost, effective and fits bike tubes/forks well. Most companies are drowning in packing materials so check with your work shipping dept for excess packing material. I go nuts packing the bike. Keep in mind you or the buyer are unlikely to ever get shipping damage covered by the carrier. So when you are thinking about paying for insurance read the fine print carefully as they'll happily sell you coverage for a $6K bike and then deny the claim because "packaging was not appropriate". Personally I have never had a bike damaged in shipping, but it is a risk. If they lose the bike you'll get paid out without a problem so there is that. I tend to not get any insurance and self-insure I figure with all the money I've saved over the years not insuring stuff when I do suffer a loss/damage eventually I'll still be ahead.