Just as an FYI for those as want to play ROTT without Dosbox, there are source ports out there that add some modern features.
1. WinROTT and WinROTTGL - Status: Active
Homepage
Adds 3D acceleration, bigger resolutions, more advanced control settings, and better multiplayer features, as well as a GUI launcher. Note: I had to download this DLL pack and extract it into the WinROTT directory to get WinROTTGL working: Filefront link
2. ROTT For Linux -Status: Active
Homepage
Pretty decent Linux port, with few extra features. Page claims it can be compiled for OS X and Win32 as well. I personally use this.
3. A native Mac OSX port:
Here
4. A port of Rott for the DS/DS Lite (homebrew):
Here
5. A port of Rott for the Dreamcast(!)
Here

I'm using WinROTT ATM, in DOSBox, the music doesn't sound as good, I get a giant black bar in the lower part of the screen and no HUD.

Those settings can be changed in the dosbox.conf file. Run the setup.exe file too to get better sound as well.

Do I have to run that with DOSBox or what?

The dosbox.conf file is a simple text file that you can edit with your favorite text editor, there you will find the settings you want to change like the apparent widescreen enabled in your setup. It's the in dosbox folder. For the sound, just run sndsetup.exe to select a good sound device.

I mean sndsetup.exe, do I have to run it with DOSBox so it'll detect the correct hardware DOSBox emulates?
About the .conf file, I found a dosboxRiseOTT.conf, dosboxRiseOTT_client.conf, dosboxRiseOTT_server.conf and dosboxRiseOTT_setup.conf, which one is it?

dosboxRiseOTT.conf, but it would be better if you change the settings with sndsetup.exe and the regular setup.exe instead. And yes, you have to run sndsetup.exe in DOSBox, since it's a dos program like Rott's .exe. Run it, and select the correct sound playing hardware. Usually it's soundblaster for both MIDI and music.

Managed to fix my sound, but what value do I need to change in the .conf file to remove that black bar?
Just adding this here, I accidentaly deleted my savegame when I went to load it. :C

Are you playing fullscreen or windowed mode? Is your screen widescreen or normal display?
BTW, I found two more ports for ROTT:
A native mac osx port :
http://www.dr-lex.be/software/rott.html
This is a really cool one, a port of Rott for the DS lite :
http://vespenegas.com/rott.html

Playing fullscreen and yeah, my monitor is widescreen.

Thanks! I actually tried the DS port back in the day, but forgot about it. Added the info.

Try setting on the dosbox.conf file your widescreen's monitor native resolution.

Change aspect=false to aspect=true. This should work in all cases, but might cause slowdowns on certain outputs.

Yes, that could help. Since he has a widescreen, his aspect ratio is not 4:3 like standard screens.

Well, changing that variable makes the screen have two small bars in both upper and lower parts instead of a big one at bottom and it cuts a little of the screen at the sides. I'd rather have the big one. :V
Thanks anyways.