Does the method of preaching from house to house have its basis in the Scriptures?

Yes.

When Jesus sent forth the apostles to preach, he instructed them: “Into whatever city or village you enter, search out who in it is deserving.” (Acts 5:42) Jesus told them to go to people’s homes, saying: “When you are entering into the house, greet the household; and if the house is deserving, let the peace you wish it come upon it.” (Matt. 10:11-14) These instructions make clear that as the apostles “went through the territory from village to village, declaring the good news,” they were to take the initiative to visit people in their homes. (Luke 9:6)

Some religions have acknowledged the Christian obligation to preach in public places and from house to house, although this is often left to a limited group of missionaries or clergy to fulfill... not every member.

However, every member who is identified as a JEHOVAH'S WITNESS heeds Jesus' instructions when he told his followers to "make disciples of people of all the nations," and when Jesus himself set the example by "journeying from city to city and from village to village, preaching and declaring the good news of the kingdom of God." (Matthew 28:19, 20; Luke 8:1)

As of the time of this posting:
Jehovah's Witnesses print the 1st & 2nd most widely distributed magazines in the world.
-Wikipedia; "The Watchtower"; Heading: "Distribution", pars.1&2
-Wikipedia; "Awake!"; Heading: "Publishing", par. 2

For more, see:
Worldwide publishing and translating

Report of Jehovah's Witnesses Worldwide

Official Jehovah's Witnesses Web Site, On-line Publications and Public Information

Sites and Pages in Defense of Jehovah's Witnesses

Search For Bible Truths - ARCHIVE 

Scriptures Index

Search For Bible Truths - Search Guide