How many steel ingots and leather strips would it take to upgrade an Imperial Bow to legendary?

1 steel ingot if you have the right skill level and smithing enchanted gear.

you don't need leather strips to upgrade it.

Does the same go for the armor?

Yes. Quality of uprgade is entirely dependent on Smithing skill-level and smithing perks. A list over each set of armor's requirement and the corolating perks for improved tempering can be found here:

http://www.uesp.net/wiki/Skyrim:Smithing
http://www.uesp.net/wiki/Skyrim:Smithing#Skill_Perks
http://www.uesp.net/wiki/Skyrim:Specialty_Gear
http://www.uesp.net/wiki/Skyrim:Unique_Items
http://www.uesp.net/wiki/Skyrim:Artifacts

Thank you.

Yes, it would depend on how often you tried. If you upgraded every time it showed as possible, you'd end up spending maybe a dozeningots. If you waited until you had hit 100 skill then you'd use only one. And if you went bug nuts working the alchemy & enchanting & restoration route to make incredible potions in order to make even more incredibly enchanted smithing gear then I'm not sure youwould EVER stop upgrading, since it's possible to make some god-like improvements - eventually (sometimes) crashing the game.