... the problem is the sports mode is too slow
Depending on what you mean by "too slow" there are a few settings you can try. But a bridge camera is relatively handicapped in two ways of being slow that probably make a dSLR a better choice for BiF (Bird in Flight) shots.
Shutter delay is too slow
If by "too slow" you mean that the time between mashing the shutter button and the picture being taken is too slow, then you main recourse is going to be using a half-press on the shutter button to get your subject in focus and the exposure settings set, before pressing all the way down to take the shot. This can sizably reduce shutter delay.
Autofocus is too slow
If by "too slow" you mean your camera's having a hard time getting the bird in focus for the shot, then you have to get better/faster at aiming your AF points on the bird and getting the lock while it's moving. You have to get better at "tracking" the bird as it circles in the skysky; or anticipating a good spot to pre-focus on. One way to help you aim the camera more accurately with a supertelephotosuper-telephoto lens is to shoot with both eyes open. Get good at anticipating the bird's movements by studying how it tends to fly, and learn to keep the bird in the frame.
Unfortunately, most bridge cameras autofocus by contrast detection--using the contrast data on the main image sensor to judge if something's in or out of focus, and since it will try both directions of focus (front and back) before it knows which way to go, it can be slower than using a phase-detection AF system that knows which direction to head for. So it's unlikely that you'll be able to snap shots of birds that don't fly in a regular pattern you can anticipate for enough time to get AF lock.
Shutter speed is too slow
If you're getting motion blur either from hand-holding the camera and joggling the camera, or from the subject moving, then the setting you need to look at is shutter speed. This is the amount of time the iris in the lens is open for the exposure. The longer your shutter speed is, the more light you get, but the more chance you have of blur affecting the image.
To combat handholding camera shake, you can use a tripod, monopod, or other form of stabilization, or you can try to keep your shutter speed above 1/equivalent_focal_length. In the case of your FZ72, zooming all the way in is the equivalent of 1200mm, you'd need a shutter speed of 1/1200s or faster. This fast a shutter speed, and the maximum aperture of the lens at this end (f/5.9) is likely to require that you use an iso setting of probably 400, if not 800 or 1600, depending on the lighting conditions.
Subject motion blur can go even higher in speed--the faster the subject is moving, the faster your shutter speed has to be to "freeze the action." I've taken BiF shots with blurred wings with shutter speeds of 1/1000s.
Right tool for the task
Ultimately, a bridge camera often isn't responsive enough to shoot birds in flight. This is why most bird photographers you see will use a dSLR. But that doesn't mean you can't shoot birds with it. Perched, standing, or walking birds are still entirely doable. And, more than any camera gear you could possibly own, your own fieldcraft abilities and knowledge of individual birds is going to be the key to getting successful bird photographs. It may be that you simply have to work on reading bird body language to avoid flushing them. Every beginning bird photographer can show you a few thousand bird-butt shots where they failed to learn that lesson. :)