There isn't a cover-to-cover Bible in many Catholic Churches for each person in the pew, but there are missal or missalettes that have the Sunday readings, and the daily Responsorial Psalm. That isn't to say Catholic "aren't allowed" to go out and get a Bible for themselves! As long as it has ALL of the books in the Good Book and it's a proper translation, Catholics can read the Bible all they want. In fact, one can get an indulgence for merely reading the Bible for more than half an hour.
A partial indulgence is granted the Christian faithful who read sacred Scripture with the veneration due God's word and as a form of spiritual reading. The indulgence will be a plenary one when such reading is done for at least one-half hour [provided the other conditions are met].