A lot of drives come with a copy of Nero or Sonic which (although cut-down versions) are OK for basic burning. Check whether there is anything in the CDs that came with the machine and/or drive. Do you need it long-term or just to do a few now? If you only want to use it for a week or two you could get the demo of Nero which I think lasts for a month. I found this http://www.burn4free.com/ with Google but would advise that you look into it in more detail before installing. On download.com there is a mention of a toolbar included which you'd need to investigate in case it is one of the unwelcome ones, and find out whether it will install without that. There are some others in this section of download.com http://www.download.com/CD-DVD-Burners/3150-2646_4-0.html?tag=dlbc - filter it by windows and Free, then see if they really are free. Another option if you have a few quid to spend is to look at what's on the cover disks on the computing magazines in the newsagents. If you're lucky you'll get the software you want plus a bunch of other stuff and a moderately interesting magazine for about a fiver.
Why not do it on your Ubuntu system? There's a DVD writer application included with the distro, and also some in the repositories. All free of course, without any nasty adware-ridden toolbars to piss you off!
Don't know what type of DVD you want to burn (data, video, etc) But for Burning data, two excellent free choices are: ImgBurn http://www.imgburn.com/ Which has an excellent burning engine, and is a great choice for simple data projects, and burning images. It's very small, only a couple Megs. Another program is InfraRecorder: http://infrarecorder.sourceforge.net/ It's a full fledge DVD/CD mastering tool similar to Nero/Roxio. It has better file layout environment than imgburn, and you can create multisession and audio CDs. However the burning engine isn't as robust as imgBurn. Either of these tools will let you burn DVD video files, but it they won't create video files from source materials. To back up DVDs that I own for my own use, I use DVDFab HD Decrypter http://www.dvdfab.com/free.htm to rip the movie to my hard drive, then use DVD Shrink (google that one) to recompress it to fit on a 4.7GB Disc. DVD Shrink is the best recompression tool I've seen. If you have video files, like AVIs, that you want to turn into a DVD, there's a free tool: Avi2Dvd http://www.trustfm.net/divx/SoftwareAvi2Dvd.html That will convert them into DVD video files. It doesn't include any editing tools, and is very slow. I'm looking for a better free solution but until then... If you want to stick several videos on a DVD, you could convert them with with Avi2Dvd, and use the re author tool in DVD Shrink.