The following are some ways to make your DOSBox behave nicely in Ubuntu.
The package for DOSBox is dosbox, and you might also want to consider using Alsa-OSS for enabling more than one program to output to the speaker. The package for that is alsa-oss.
If you would like to enable more than one program to use the speaker, all of them will need to be loaded with aoss.
Right click on any .COM file and select Open With Other Application. Select Use a custom command and enter aoss dosbox -exit . Make sure there is an extra space at the back. This will enable you to double click on any COM files to automatically load it up in DOSBox. When you exit the program, the window will automatically close as well. Now this feels much closer to Windows!
If you want to stop the window from locking your cursor, look up Dosbox.conf for how to set autolock=false. If you have games that you need to move your cursor to the edge of the screen, this can be annoying if autolock is off. You can always toggle it on or off using <CTRL>-<F10>.