I've done both the bassinet and as a "lap baby". The first time I flew from China to the US by myself with my 7 month old. I was lucky and he slept almost the entire 13 hour flight. I hadn't asked for a bassinet, but they offered me one after I got on the plane (this was with United). I didn't use it and just let him sleep with me the whole time. Which was great since he slept.
Also on the return flight, now with my husband, we also didn't use a bassinet and my son slept about half of the flight and the other half we shared walking with him up and down the aisles of the plane.
When we went back to the US for Christmas we flew Korean Air (very good experience, the flight attendants were very friendly and helpful, willing to hold him to give us a break etc.) This time we also got a bassinet. It worked well while he was sleeping, but it's a nuisance with watching TV. The way the airplane we were on is set up the seats where bassinets are available are facing a wall not other seats. So the TV isn't in front of you, but on an arm that pull up from the front of your seat. You can't put it up or down with the baby in the bassinet.
Overall my recommendation is, if your baby is ok sleeping with you holding him/her and you and your husband agree to share the responsibility I wouldn't get the bassinet.
I don't know if you're familiar with Korean culture, but be prepared for the flight attendants to be very gracious and quiet, while providing great customer service.
As a side note,If you don't like Korean food always order the western option. On one of our flights the said the meal was a noodle dish, which it was, but it was topped with raw salmon. It was good, but unexpected.
I just read the woman who recommended the car seat, not a bad idea for the reasons she listed, but depending on your destination and the duration of your stay you may not need a car seat. Not all country's require them (China and Korea are two that don't), plus if most of your travel is going to be by taxi or other public transportation if might be more of a hassle to have the car seat than not. I know that it goes against what we've had ingrained in us in the US re: car seat safety, but my son is almost one year old and he's only been in a car seat when we've been back in the US for the two trips I mentioned.
Hope this helps.