Bouncing is not the only option. It creates strong shadow under the chin, it is in fact much better than straight-on flash, but there are other alternatives.
Try to find a white wall or a white curtain, or a relatively white surface would do. For me, I consider bouncing off a white wall a much better option than bouncing off a white ceiling.
The light will be the size of the wall, and it will warp around the face much better because the light is shinning on the subject in all directions, not just from above (the case when you bounce off a ceiling).
Also, you can easily have your subject move closer/further away from the wall. The closer your subject is, the softer the light will appear. Obviously you do not have this control when bouncing off a ceiling.
If there is no white wall or surface, there are still a few things that you can do.
Take the flash off camera is a great thing to do, position it at an angle will give you a very dramatic photo. The shadow will still be harsh but at least the face is not as flat as straight-on flash and will look more dimensional.
Look out for light modifiers, they claim to be extremely useful in softening the light, but in fact they simply do not.
Say a flash head is the size of a deck of card. A light source so small will create harsh shadows, everybody knows.
Say you have a light source that is as big as a piece of A4 paper. Chances are, the light will still be pretty hard.
One very important thing to bare in mind is the distance between the light and the subject. If the subject is far away, even if the light is the size of a t-shirt, there will still be hard shadows.
If the light is 2 feet away from the subject's face, however, you will see a significant difference between using bare flash and using a light source that is the size of a t-shirt.
You want to bounce off a wall or ceiling because you get a massive 10 x 10 feet light source. Tiny light modifiers will never be able to match the softness of such a huge light. So do not expect it to create wonderfully soft light, it won't. It is an improvement, but not as big as what the packaging may claim it to be.
If you can find someone to hold a reflector for you (those giant 42 inches ones), bouncing the flash off the reflector is a good idea(and better than those tiny diffusers or omni-whatever). You can be very close to the subject (very important!) and you can control how high the light is.
If you can take your flash off camera (cable or wireless) then you can also use the reflector for some very good fill light.
If you don't like a reflector, or they are overpriced (I have seen a reflector costing US$60 before), you can get a piece of styrofoam. Go to a stationary store, get a piece as big as a small table for only $1. It is white, it is light and sturdy and can be easily cut into any shape and sizes. Only downside is it cannot be folded.
I have had my subject hold the giant piece of styrofoam (3 x 4 feet or so) for some fill light and the result was quite good. Can be a solution when you do not have an assistant.