In one cell, do =countif(range,">0")
For range you will want to include the cells that have the scores in them, so like A2:G2 would include cells in row two, columns A through G. The countif formula will give you a total of the cells in which a score is entered. You could label that column Total Games Bowled, or something. Let's say this goes in cell H2 at the end of the row.
In the cell to the right of that column, do =sum(range)/H2
The range in this would be the same as the range in the formula above, so it would total all scores listed. Then it would divide by H2, which is the number of games bowled.