Auto open textmate project on startup
By default TextMate should open the last open project or document - but it can be switched on/off - maybe it is off by you ??

Here is how to switch the feature on/off: http://manual.macromates.com/en/expert_preferences#oakdisablesessionrestore


  22.7 OakDisableSessionRestore
  
  When you launch TextMate it will open the project / document which was open when you last exited. You can however disable this feature by running:
  
  defaults write com.macromates.textmate OakDisableSessionRestore 1


This means that you should run the above line in a Terminal - with a 0 instead of 1