What was your OG and what yeast/ fermentation temperature? If the temperature in your fermentation room hasn't changed then there is a good chance you're done. Take a sample and if the number is right, it tastes good, and it's clear then bottle it.
I have a 1.036 batch of second runnings that fermented out w/o noticing a single bubble of the airlock- it's cold crashing and I should be bottling it a week from brewday. Don't wait longer than you have to for beer.
As for opening the bucket- there are professional breweries that ferment in open vessels. Anchor and Samuel Smiths to name a couple. If your room is clean- no mold/ fruit flies (especially fruit flies) then you have nothing to worry about.