When I make coffee with my Bialetti, there is a bit of coffee grounds in my cup. Is the coffee too thin ? On the package is written that it is fine for the Bialetti machine.
The reason is that your coffee grounds are too fine. Your Percolator needs coarser grains for various reasons:
- Allowing water trough it more easily – else the pressure needs to go too high and your coffee will taste burned as it is roasted a second time from the overheated filter basket .
- Not allowing small small grounds to "whirl" up in the water and reach the top  and flow into your final coffee.
In addition to this and if above does not help, you can —if needed— still go with what @Ecnerwal suggested as a last ressort.
 You can avoid a good part of this by using very warm (non boiling) water, instead of cold water. This means the water will boil earlier and the grounds will not get exposed to too much heat over a longer period of time.
 Do not over–power your stove. When I cook my coffee, I turn the (electrical) stove to between level 7–8/12. Using a lower heat not only makes the coffee drinkable and removes a lot of the overly strong and often bitter taste, but also prevents smaller grounds to whirl up as the water has less energy, moves less and allows smaller grounds to sink back into the filter again.
Don't worry, you've taken your first step to solving the problem. :)
If you find grounds in your cup, and you grind your own beans, simply grind your beans a few clicks coarser on your next brew.
But if you've already purchased a bag of ground beans, then try to have them ground a few clicks coarser next time. :) You'll get your clean cup real soon!