I just put it on the plane. My Handlebar bag is my "personal item". One rear pannier is a carry-on (if free, otherwise it is my 2nd checked bag). The other rear pannier is my 1st check bag. I tie the front panniers (if I am using) together so they are one unit and it is my 2nd (or 3rd) checked bag. The rack pack goes in the bike box. I try to fly Southwest due to the baggage allowance IF I am flying. You can always ship just one bag if needed as the cost for a 3rd bag can be quite high.
You could ship too. Greyhound is usually relatively inexpensive to ship stuff but typically only ships station to station. If using UPS or Fedex, ship to a hotel you will stay in at your arrival city.
Depending on where you are and your time constraints, I have found that renting a minivan or smaller SUV is actually not that bad. For instance, I am doing a tour this spring come hell, high water, or virus, from Atlanta to Charleston. The cost to fly with bags (as described below is $140 + $75 for the bike. Plus I have to get from the airport back to the actual start in Smyrna (where the last tour ended) say $5 in mass transit fees plus a hassle dealing with the city bus. So say $220 total. Plus I have to box the bike and reassemble it and hope the airline didn't break anything. I would arrive in ATL around 11am but realistically by the time I got to the hotel in Smyrna after reassembling my bike at the airport, I am look at around 3:00pm. Not bad. Would probably not start riding until the next morning around 9am. If you have multiple travelers, there would be no cost savings.
For comparison, I can rent an SUV for $136 directly to Smyrna (takes about 12 hours of driving so one long day). Figure $75 gas and tolls. Total is $211. I would probably arrive around 8am at the car rental drop off location and be on the road at 9am. If you have multiple travelers, you can save a lot since you can split a $153 minivan three ways (about 3 bikes, 3 people, and gear is max unless you disassemble the bike. So if going as a couple, the cost would increase to ~$220 or $110 per person.
For me, I will drive instead of fly since I can just put the bike fully assembled in the back of the SUV, put the bags in and go. Reverse to start riding. For me, the extra time savings on flying is just used up by boxing the bike and reassembling the bike.
If you have access to Amtrak with roll-on bike service, that can be another easy way but Amtrak can be a bit pricey at times.
Tailwinds, John