getting around sans car rental in Croatia/Slovenia

It entirely depends on where you want to visit. Along with catamarans and ferries, bus is the primary public transport (limited train service). The overall gist is that along the coast transport is easy, going inland it is more complicated.
Even if you had a car, Ljubljana to Split is a five-hour drive so it is not going to be quick by public transport.
If you share your wish list, we can collaboratively help you.

If you do not have a full itinerary yet, you'll want to at least narrow it down. Do you want to cover any of the land locations that the bike tour skips over by sea?
Are you interested in inland Istria? (Again, bus is great along the coast, but to visit the hill towns you will want to book a private driver or a small tour).

If the cycling trip went from Dubrovnik to Split, you'd have more options for exploring
post-cycling. Since I suspect your cycling can't be reversed, one option would be
to do your exploring before the cycling. Start in the north, end up in Split and start
your biking, fly home from Dubrovnik. Perhaps not optimal, but given the situation,
you are looking at a non-trivial amount of backtracking.

Or, just construct an itinerary that focuses on Dubrovnik, Mostar, the islands, etc.

If you are ending in Dubronik, then unless you backtrack your options in Croatia are limited. But who said you have to conform to borders. The Bay of Kotor is 1 hour from Dubrovnik.

Thanks for the input, and I should have been more explicit. Mostly we want to take advantage of being in a region of the world we've never visited before, to learn and experience culture/history. The cycling trip can't be changed regarding the Split/Dubrovnik start and end points. I'm thinking that having spent a week along the Dalmatian coast, we'd like to be inland for the remainder of our stay. Which is why I thought of flying into Ljublana and out of Dubrovnik. It was just how to get from L. to Split that seemed complicated. Looking at some online sites it seems you shuttle to Zagreb and fly to Split or bus the whole way. Bus trip looks like most of a day, but maybe it's the "journey not the arrival" - any clue how busses are in this region (on time? easy to reserve?). I think we could figure out interesting day trips in Slovenia before heading to Split. Thanks again -

Mostly we want to take advantage of being in a region of the world
we've never visited before … The cycling trip can't be changed
regarding the Split/Dubrovnik start and end points … I'm thinking
that having spent a week along the Dalmatian coast, we'd like to be
inland for the remainder of our stay …

Don’t let borders limit you. Montenegro is less than an hour from Dubrovnik. Don’t go backwards, fly out of Podgorica. Here are the inland destinations. For videos of the coastal destinations visit: https://community.ricksteves.com/travel-forum/montenegro/podgorica-to-dubrovnik-by-car

Montenegro Places, Inland
Gusinje https://youtu.be/-DOZ2-U9yUw?si=-yOpR723rlEsJIK7
High Country: https://youtu.be/TC8q0G8JxZE?si=PDJQIK7lJwoGQrAe
Ostrog Monastery https://youtu.be/ixrJu6qv46M?si=WML9Hs2hOQCsKZwE AND Hotel & Restaurant Sokoline https://youtu.be/miNV1FVK7qI?si=iZC_lViMUEk6JGI
P1 Mountain Road https://youtu.be/QSz5hZVNxQ8?si=kAUpMBWDbSSztzt5 AND Prosciutto at Zora https://youtu.be/08il6EXog3o?si=PkQ6Rrueu6c_-U98
Stari Bar, https://youtu.be/OBU56OT78fw?si=tzF65lSmOXSEpWKZ
Tara River Canyon https://youtu.be/9aGMZB8hB5Y?si=NFKsf6YtGAX2uVCa AND Motel Tara MB https://youtu.be/wGuRybkymEI?si=TGgevmpFSCGTghPq AND Rafting https://www.youtube.com/watch?v=Hh4KPo8HtZY AND Zip Line https://www.youtube.com/watch?v=WwnHZC4Ss08 AND Fly Fishing https://youtu.be/MpnDIoqvfbo?si=4N-_ez7vaGsdFQm-
Rakia https://www.youtube.com/watch?v=-W-rTt8hUNY AND Wine https://www.instagram.com/winery.garnet/

OR

Fly out of Podgorica and catch a discount direct flight to Budapest :-) $80 and 80 minutes.

I spend significant time in northern Croatia and Slovenia. It is impossible without a car to get to the places you will want to see. There are virtually no trains covering this area, so people without cars rely on buses - buses which won't always go where you want to go.

Do yourself a favor and rent a car. The roads are great and the drivers are courteous.

If the bike tour skirts the islands but skips over the mainland, it would not necessarily be duplicative to explore southern Dalmatian, but if arriving Ljubljana, you could do something like this:
Arrive Ljubljana, do a loop to one of the lakes and back, roughly five days
Bus to Zagreb, a few days depending on day trips, possibly stop at Plitvice
Bus to Zadar, possibly see Sibenik, possibly Krka
Bus to Split, start tour

There’s almost no avoiding at least one long bus ride if you’re going inland to the coast. If you were flying into Ljubljana, it’s a couple hour bus ride to Zagreb, which is a few more hours bus ride to Split. Ljubljana is a great base for guided tour day trips. There are quite a few out there and imo look a good value. Lake Bled is pretty easy as a DIY.

Flying into Zagreb is generally a cheaper alternative. A couple nights there would be nice, and there’s plenty of bus connections. You could break up that trip to Split with an overnight in Plitvice. It can be a tricky connection but it’s doable and well worth it imo. If all else fails, a quick plane ride from Ljubljana or Zagreb to Split is also an option.

As pointed out, by bus Ljub to Zagreb is about 2.5 hours, then Split is 5 or 6 hours. Spkit to Dubrovnik is another 4.5 hours. When I did this i hired a driver/guide that reduced travel time 25% and provided a lot of flexibility.

On the otherside of Dubrovnik you could go by bus from Dubrovnik to Kotor to Budva to Ulcinj by bus in under 5 hours, and 25% less with a driver that will be less expensive than in Croatia.