What would a woman Rising Scorpio with a Scorpio Sun and Libra Moon be like?

Inwardly intense, outwardly reserved. Tries to stay balanced emotionally and be pleasant, but often finds there is an inner struggle. Tries to be impartial and fair, and generally succeeds.

However, you have only given 3 out of 40-60 factors from the chart. The rest of the chart will definitely affect what i have said above ... especially whatever aspects are made to the Sun and Moon by other planets in the chart. Aspects will bring out the "best side" or the "worst side" of the sign, depending on the type of aspect that is made by the other planet.

Also, Mercury, Venus and Mars are as important as the Sun, Moon, and Ascendant in determining the major functions of our personality.