Is Uber widely available (and safe to use) in these countries? If so, is it the same App we use in the USA? We are a family of four.
Uber uses unlicensed drivers and strives to escape regulations at all costs to gain market share...how can anyone vouch for a random driver's safety record? That person is not even considered an employee of Uber because Uber doesn't define them as such. You basically have to put your faith in this (IMHO) highly unethical company. If you want to still use them, then go on the Uber website and see what cities in each of the three countries they serve. Bosnia is so inexpensive that I wouldn't hesitate to use a cab there (I took one from Sarajevo Airport to the old Turkish quarter). Public transit is also very inexpensive and it works fine.
I used Uber twice (because Lyft wasn't available; I generally avoid Uber) in Dubrovnik and had no issues (traveling alone) and it was very inexpensive. But as Agnes said, it's impossible to tell you they are safe, just as I wouldn't tell you it's completely safe to use them in the US. I met someone who used Uber in Split and had no problems either. And yes, it's the same app.
To carry passengers for a charge, a driver needs a paid permit. Croatia, like our neighbour countries, has lots of drivers (including Uber) offering their service without a permit. Their charge is low because they don't pay for a permit, because of this we have the biggest problem of all, passengers are NOT insured.
No Uber in Slovenia, it's currently illegal or better yet, the legal requirements are currently too costly for Uber to enter the market. However, taxis in Ljubljana are cheap. The cheapest and safest way to get a taxi is to call a reputable taxi service (I recommend Taxi Laguna) and they will send you a taxi straight away at a reduced rate compared to hailing one on the street. You could also use an app called Hopin, which is similar to Uber, but uses licensed taxis. Beware of taking a random taxi on the street as taxi companies can set their own prices in Slovenia, so you may end up paying a lot more than you bargained for. Otherwise, the average rate in the city is about €1 per kilometre.
In rural areas, taxis are more expensive and not a particularly good deal as the distances involved are often larger. With a family of four, I would also look into car rental as an option of getting around outside of cities. Public transport can vary from excellent to nonexistant, depending on the route, but within cities it is generally of good quality.
Thank you everyone. I think we'll steer clear of Uber. We'll call ahead for taxis whenever possible. We will have a rental car at a few points in the trip; but sometimes it's just difficult because we are traversing three countries often and picking up the rental in one country and dropping it off in another country proved too expensive. I have pre-booked several bus trips via GetByBus. I leave very little to chance! We are leaving in about an hour; can't wait to get to Dubrovnik tomorrow!!!