This depends what time period you refer to. Bushido was a not formally written till the Tokugawa period at a time of peace and rigid order. During the Sengoku Jidai, Bushido was thought of as mere guidelines in a similar way to the "chevalerie" of the middle age Europe.
Ninja, or shinobi, were foremost spies. As such, of course, they had no honour and no morals! Unless, of course they were in your employ. In that case, they were another weapon in waging war. Oda, Toyotomi and Tokugawa were famous for using ninja -- after getting bitten by not using them.
Stephen Turnbull is a good source for this, Ninja AD 1460-1650 (Warrior) in particular.
See this question on history.se for the role on ninja during the Sengoku Jidai.
After the OP edit. In the same way as you cannot be a chivalrous Knight of the Round Table, you cannot be a Bushido Samurai. The samurai class does not exist any more after the order of Emperor Meiji on the 7 April 1868. I am not aware of any such order regarding the ninja clan. So, I guess you could follow a shinobi-do but I am unaware of any such thing being formally drawn -- more like guidelines really.
The definition of ninja as "a warrior without honour" is erroneous. It literally means hidden person, see this page for example but the wikipedia article has it too.