If you really dont want to go to the doctor then like said, clean it really good. If it stops bleeding I would use supper glue to hold it together. Less chance of scaring and band-aids with a wrap. I would also get some SILVADENE (silver sulfadiazine) cream. You can find it on amazon and it helps a LOT with stooping infection. A light coat of iodine is helpful also but be careful. I put it on to strong once and it peeled the skin.

Make it a light coat.
No for some comparison, that's not a cut, this is a cut. It's of 6yr old daughter after she put her hand through a single pane glass window pushing on a door to open it at the neighbors. She never cried until they gave her shots to numb it. It also cut 3 tendons clean off and ran next to the main artery. Still plenty of blood but due to me showing her just 2 days prior how to stop bleeding by putting pressure on a cut and wrapping it ASAP because I got a small cut (compared to hers) she knew what to do immediately.
I had one of those old disposable camersa in the glove box of my car so after getting her to the hospital I took pictures to document it.
<img src="http://forums.steroid.com/attachment.php?attachmentid=138546"/><img src="http://forums.steroid.com/attachment.php?attachmentid=138545"/><img src="http://forums.steroid.com/attachment.php?attachmentid=138547"/>