DOSbox works for running gwbasic, and many old dos programs.
To install it: sudo apt-get install dosbox
To run it: dosbox gwbasic.exe
Caveats: DOSbox emulates the CPU, so it runs apps slower than on Wine or as a native app. However, anything that originally ran on a 486 should run fine with DOSbox.
Speaking of gwbasic, by default it saves the source in a binary format.
You can save in a text format with the a (ascii) switch, like this:
As far as a basic interpreter that runs gwbasic code on Ubuntu, I haven't found one yet, but I am still looking.