I had to talk a friend out of buying a bridge camera a few weeks ago.
The quality from some bridge cameras these days is actually pretty impressive. They've generally got plenty of megapixels for normal use, respectable focal-length range on the telephoto end and some have video features / frame rates / resolutions that much more expensive DSLRs don't have.
They tend to be limited on wide / ultra-wide angle and their ISO performance isn't as good as the larger sensors but presumably for a safari neither of those things will matter too much.
Where they won't be as good as a DSLR for safari is having the autofocus speed and shutter responsiveness to quickly focus, track a subject and fire off a bunch of accurate frames in a short space of time.
My biggest criticism of bridge cameras for someone wanting to get into photography is (and always will be) that you're paying for a camera that will be surpassed by something better in a couple of year's time. At that point, your camera (and the lens built into it) lose all their resale value and unless you stick with that camera until the end, you'll eventually put it in the bin and buy another one.
Using DSLRs can seem like a waste of money at the entry-level and it's not easy to convince someone that buying something higher-priced now will pay dividends for them in the long run. Of course, if you think they're just going to use the camera for this one holiday and forget about it, let them buy the bridge camera. Or better yet, a used DSLR from 3-4 years ago with good autofocus & FPS and a used, beaten-up Sigma 50-500.
