A Bush-buddy is a definite no-no. Don't even consider it! Nepal has serious deforestation issues caused by villagers burning extra firewood for trekkers. It may not even be legal to collect wood, and you have pretty much zero chance of finding any in much of the mountain regions anyway.
If you want to be able to "refuel" in the Khumbu/Gokyo region then it is likely you will only be able to get hold of kerosene… or it's possible you might find some gas canisters in Namche Bazaar. So I'm not sure you'd find fuel for an alcohol stove… you'd probably have to find some in Kathmandu, which would defeat the purpose of carrying a light stove.
The other problem with the alcohol stove method is that there are some question marks about how well it will work at 5000m. The whitebox stove claims to work up to 4000m (tested by users) but that doesn't mean it works well. It can be really windy in some valleys up there, and I wouldn't want to rely on an alcohol stove to cook my dinner.
If you're camping in Khumbu/Gokyo it's going to get bloody cold (unless you are going in the monsoon!) which means that you would need to keep gas canisters warm before use (they don't vaporise properly below -10C I think).
The other option is a whisperlite or one of the coleman stoves with kerosene. I really do recommend the coleman peak 1 for reliability… but I've never used it at 5000m! They can pump out a lot of heat, and the peak 1 does pretty well in the wind (it's not as 'open' as the whisperlite). Plus you can use a lot of different fuels with it (but don't use it inside your tent!!).
Anyway, let me know if you have any other questions. I've spent a couple of months around Everest/Gokyo/Chukkung region but didn't take a stove last time I was there, and didn't camp. You better have a bloody good sleeping bag (at least -30C I'd say)!!