In TextMate 2, I can run the current file by pressing CmdR, and it will show in a new area under the text editor.
But how can I close it?
You can click it and press command-W.
I haven't found any keyboard shortcut for closing it or moving focus to it though. If you set Preferences > Projects > Show command output to New window, you can close the window with command-W and move focus to it with command-`.