It’s possible to take bikes on trains, buses, and some ferries in Croatia.
The trains didn’t seem too bad although we didn’t feel particularly welcome. The rail network in Croatia doesn’t have a lot of coverage though. As with Slovenia, you might have a bit of trouble getting on the trains with a bike if it’s particularly crowded.
Buses will accept bikes, but only when they’re in the mood, and it’s up to the driver. You have to wait until the bus arrives, and if you’re rejected try the next one. If the bus is not very full you have a good chance, so try not to travel in peak times. The charge for taking a bike is considerably more than for the same size of luggage, as well.
Car ferries are great for bikes, but the passenger-only catamarans won’t take them. There’s no reason why not, so, as with most things, this might be negotiable. You may also be able to negotiate with tour operators and the like if they are travelling to an island you want to go to. To be sure ahead of time, check that the route you want to take is serviced by a car ferry. Also, in some cases the cost of a bike on a ferry is more than the cost of a person.
In Slovenia we never tried using buses, but we used trains fairly regularly and never had a problem. We weren’t travelling in a peak time though, and I understand you can be rejected by the train conductor if he thinks it is too full.
In general, travelling outside of peak season will give you a good chance of getting onto public transport with your bike.
We never had to box or bag the bike on any trains, buses or ferries. Just take the front wheel off for the buses.