I’ve traveled with my road bike and triathlon bike, separately, since 2016. I’ve taken them on many planes, some trains, buses, boats, and cars. I take a bike pretty much everywhere I go. I’ve never regretted it. It’s wonderful how much more you can explore with your bike. You’ll go places you otherwise wouldn’t.
I’ve even picked up an indoor trainer (Wahoo Kickr Snap) and took it with me to a couple of places. But that’s another story.
I pack my bike in a Gavilan BFF bike case from Radicalvelo. The case cost me $475. However, it appears they no longer sell it. My friend, though, has the Orucase Airport Ninja case, that is about the same size as mine. It’s a nice case.
To pack my bike, I have to disassemble it: handlebars, fork, rear-derailleur, brakes, wheels. It takes me about 30-50 minutes to disassemble/pack and unpack/assemble. I’ve done it so many times now, I’ve gotten very comfortable doing it. I also adjust my brakes and derailleurs after re-assemblying it. I also have a small tool bag with hex wrenches, screwdriver, something to take the peddles off. I used to disassemble my chain but now just wrap it and the rear-derailleur together and attach them to the bike frame securely.
My bike pump also a bike stand: Topeak TRANSFORMER RX. It’s very useful and lightweight.
I highly recommend having a portable digital scale to weigh your case and other bags!
Regarding transportation fees: My case is always less than or equal to 20kg (45lbs). The dimensions are close to the maximum allowed. Nearly every international flight has a check-in allowance that allowed me to check-in my case and another bag without any additional fees. Out of the many flights that I’ve taken, only one airline (Avianca, international flight) counter agent has measured the case dimensions and made me pay an oversize fee over $100 (I can’t remember exact amount) for being 10 inches over. For budget airlines, some of them charge per kilogram over some minimum or something similar. Usually, the additional cost is reasonable; much less than $100, maybe around $20. It’s always best to pay the overweight fees ahead of time, if any.
There was a time where I had taken my assembled bike onto a boat and they charge me a small fee. Also, a similar thing happened when I had to take a long distance bus somewhere.
My wife uses a bike box. For me, the box is cumbersome because of the size, however, the bike is faster to pack and unpack. She’ll pay the oversize fee when necessary. But, she hasn’t travelled many places with it and so far the costs have been fine with us. Actually, some airlines sometimes have an no-fee allowance for bikes! So check the airlines for their policies.
Overall, I think you should take the bikes for the amount of time you’ll spend in one spot.