Airlines won't take more than basic hand luggage for free, but sports equipment is normally clearly defined and welcome in the hold when prebooked.
I used to take a bicycle by train but have given up any idea, it's just too complicated and unreliable. Yes, it's free, but that's all that can be said for it.
It goes in the car every time now.
I've flown with a bicycle many times. The rules keep changing, but are relatively straightforward. Look on almost any airline booking web site and bicycles, surfboards, golf clubs, etc are welcome, but prebooked and paid for. Until covid, my bicycle was due to fly again this year, but that idea got canned. I don't have a surfboard but the same criteria would apply to my decision process.
Exactly; you can't just turn up with one and expect it to be carried. It has "faff" associated with it.