It's not so much the camera as the photographer, in my opinion. Some of my mates who I would rate as very good photographers can do wonders with the camera in an iPhone whereas I am sometimes disappointed armed with a decent SLR.

I would say, if she's keen, take her along to the local camera club. They often run courses for beginners to get them started with the basics and this will make a real difference.
As to camera choice - that depends on the type of photography and what she's prepared to lug around. Macro shots of insects up close, action shots of motorsport and night photography require the flexibility of a digital SLR but inside those extremes compact and bridge cameras can come up with decent results, are much cheaper and easier to carry.
The problem, IMHO, with compact cameras these days is that most have dropped any kind of viewfinder and it's just a joke trying to frame a picture (and hold the camera still) with the camera at arm's length peering at the LCD screen on the back.
A bridge camera is much more awkward to lug around but at least most have an electronic viewfinder.
Remember that photographers like to upgrade. The second hand market is therefore quite good. Compact cameras are a bit too fragile to risk it unless they are cheap, IMHO, but for a nice bridge or DSLR, second hand might be worth a look.
Kevin