Quite right. PowerPoint is not meant to produce artwork for professional printing. It is not even a postscript program, although it can produce acceptable PDFs if you use the right settings (basically all quality and size options on max).
Usually in these cases I reduce the size of the PowerPoint PDF within generous margins on the page. The margins are either left white or filled with a compatible flat colour to bleed off.
If you really need bleed here is how I would do it. Produce your slides with the chosen background, then produce another copy without the background. Make a PDF of both sets, as well as one with just the background.
Send these files to someone with InDesign who will be able to enlarge the background on its own to bleed off. The PDF of the slides without a background can be placed on top, overprinting if necessary. This may produce unacceptable results where coloured text or graphics in the slide is affected by the background. A rectangle or other simple shape can be masked from the background with a white box on a layer in between. If you have any white out text this method will fail.
The results from all this work will be different from the original slides, and the quality will inevitably be below the normal standards for professional printing.
That is the quick and dirty way to do it. The proper way to do it is to supply someone who uses InDesign with all the text, graphics and pictures used in the PowerPoint slides and ask them to reproduce it in InDesign.