Bridge cameras can be ok. Sony and Panasonic make good ones. They aren't as good as a DSLR because their sensor size are smaller and their lens (while very flexible) is optically only "ok" because all-in-ones have to make compromises.
The thing about bridge cameras is they are for wide to long. If your wife enjoys that, then it might make sense. If she takes photos of landscapes, flowers and such then a camera with a long lens is just paying extra for a more compromised lens.
DSLRs remain the best at photos, but they can be off-putting to new users to their bulk, weight, cost and the need to change lenses to get the perfect shot. But they produce the best results once you master them. I am not very sensitive to weight and so I sometimes lug about 4-5 lenses (with a similar amount n the trunk, in case I change my mind about what I want to shoot), a camera body or two, and maybe a tripod or some lights. It adds up. Cost, weight, inconvenience, and so on.
If you want to split the difference, the m4/3 line up is not as good as a DSLR but better than any bridge camera. The cost won't be much less but they tend to weigh a little less and because the sensor is smaller, the bodies and lens are a little smaller. Quality optics are fewer to chose between. You can't get the same very thin depth of field a DSLR can. But they can do a very good job.
Alternately you can get a smaller pocket camera with a larger sensor which will then split the difference between m4/3 and the cellphone. The good ones are costly, but they make models which can fit in a purse.
Talk it over with her and I can give you some pointers on what to look at in the category she likes.