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I think you may be talking about a cheap room in a motel or hotel. But I usually see it "two-bit room". I believe a "bit" is a monetary term, meaning about 25 cents.
Two bits equals 25 cents, so a four-bit room costs 50 cents. In "King of the Road," he's referring to a very cheap hotel room (often called a "flop house").
The Following User Says Thank You to Ouisch For This Useful Post:
Thanx for the help susiedqq, I have checked with other sources, one bit equals 12.5 cents. In the song titled 'King of the Road' the room really costs 50 cents. Cheers: Andycat
King of the Road 
Cheers: Andycat
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