Why is wiretapping called "bugging" and since when?

Bug, meaning "to arm something with an alarm" is from 1919 and this sense is mentioned as the forerunner of the word bug, meaning "to attach or install a listening device". Thus, it is not exactly true that the origin of the word bug, bugging in the sense asked in the original post is from 1919.

It is mentioned in the book 20th century words (by John Ayto):

Here is the excerpt from 1919, from the original source:

The earliest origin is mentioned as 1935 in the books 20th century words (by John Ayto) and Merriam-Webster's Collegiate Dictionary: Eleventh Edition but I couldn't find the actual reference.

In OED, the earliest reference is from 1936 for the noun and 1955 for the verb.