Will she take me back?

Recently my g/f of 4 months broke up with me. We have known eachother for 6 years and just started dating seriously. One night at a bar a girl came on to me very strong and I mistakenly gave her my number. She called me once and I answered it and talked for a few min and told her I had a Girlfriend we didnt talk for about 3 weeks when she called again but i didnt answer then she started sending me text messages and I replied to those. Another night further down the road I was slightly intoxicated and got a little ual in one of the text messages. My girlfriend found it and broke up with me. I realize that the impulsive act that did not benifit me in anyway was 100% not worth it. I have been constantly talking to my now EX trying to get her to take me back... i know i dont deserve it but I will honestly not do that again... What should i do to get her back.