There is a unique ministry called the Pocket Testament League dedicate to sharing the Gospel of Jesus Christ. 

The Pocket Testament League has, for more than 110 years, motivated Christians to read, carry and share the Word of God. Begun in 1893 as the vision of a teenage girl named Helen Cadbury, the League provides free resources empowering people to develop a lifestyle of personal evangelism.

You can get free copies of the Gospel of John with various covers and translations.  You can order all you like (they do accept donations, but it is not required).  If you are able to strike up a conversation with someone on spiritual matters you can offer to give them a booklet.  It may be less intimidating to the other person than if you gave them a whole Bible to read (though that is good, too!). 

As noted in these 8 Witnessing Tips, it is helpful to leave them with something. The Gospel of John is considered one of the most beautiful works of literature ever written, and of course it was inspired by the Holy Spirit.  As John himself wrote,

John 20:30-31 Jesus did many other miraculous signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.