I know there is an application that does what I want. It's called
gmrun
But I was wondering if I could get something like bash completion with unity's run interface .i.e. with tab command ?
Submit a bug report against unity-place-applications
as that is a wishlist item. There is currently no option in Unity for tab auto-completion to work on the Alt+F2 screen.
This doesn't work with current Unity (as you already found out).
However, if you post your idea to http://brainstorm.ubuntu.com/ or present it on the Ayatana mailing list, some developer might implement it (however, don't count on it landing in Natty).
There's no way to do this in 11.04.
Hopefully the whole of Alt+F2 in the Dash will be refined over the next few releases, because at the moment it is lacking compared to the old version.
See also Bug #736222: cannot paste into dash.