Black Soldier Fly larvae, aka Phoenix worms

Actually a BSF unit must be outdoors to facilitate reproduction, it's not a closed system. The adults mate in flight and with the exception of very specialized systems this is best left to free flying BSF. Even if you didn't mind BSF pupating and mating in your living room they require fairly intense light for good reproduction.

I'd assume a screen enclosure would not work either?

I am currently a 2nd floor apartment dweller. I bet I could get a way with a under desk clothesbox unit but don't think it would fly well amongst the neighbors plants etc...no pun intended.

I'd assume a screen enclosure would not work either?

I am currently a 2nd floor apartment dweller. I bet I could get a way with a under desk clothesbox unit but don't think it would fly well amongst the neighbors plants etc...no pun intended.

A screen house is fine if it's warm enough and they have about 10 X 10 X 10 feet, maybe less. I'm not sure how the neighbor's plants figure in though... Unless the neighbors have rotting food waste on their balconies I doubt they would know that you were cultivating BSF. I know a person on the eight floor in Houston who attracted and cultures BSF there.

I have been raising a few in a 5 gallon bucket and while they are doing well I haven't seen any eggs/new ones. Is this a bad sign?

Also, what do I do to allow them to pupate(assuming you might have to let some make it to facilitate restocking your culture).

On the linked blog he mentions allowing the mature worms to burrow in soil, so if you have a self-harvesting bucket set up as suggested, just take some of the ones that are in your collector (since they crawled out looking for a place to pupate) and drop them on the ground. Make sure your bucket has a way for adult flies to enter and you should be set.

I have been raising a few in a 5 gallon bucket and while they are doing well I haven't seen any eggs/new ones. Is this a bad sign?

It's not likely you would notice new larvae for a couple of weeks; the eggs take four days to hatch and the newly hatched larvae are only about 2mm long. Eggs are fairly easy to see if laid in clusters, but often the females just scatter their eggs individually which makes them almost impossible to see. If you place strips of corrugated cardboard around the bucket the BSF are likely to lay clusters of eggs in voids.

Also, what do I do to allow them to pupate(assuming you might have to let some make it to facilitate restocking your culture).

You don't have to nurture the mature larvae through pupation but if you want to build up a dense colony of larvae it's advisable. Here's something I've written for those who want to maximize their colonies:

As the larvae mature

The dark mature larvae will gradually accumulate in the collection bucket. In an established colony you could feed these larvae to pets, livestock or wildlife, but when starting a new colony they should be allowed to pupate into adult form (winged stage) and mate. A typical BSF unit is not a closed system which means that the adult BSF are released so they can mate outdoors and then return to the unit to lay their eggs.

A BSF unit at full capacity will have enough larvae in it to cover the surface area with few inches of solid larvae, maybe more. Until you achieve that density you should focus on building up the colony. I don’t recommend feeding any mature grubs to animals until you completely establish the colony. Each pair of BSF that you sacrifice as animal feed represents 500-900 eggs that might have been laid in your unit. I also don’t recommend scattering the mature larvae on the ground while building up a colony. I think it’s best to protect every mature larva until your colony is at capacity.

If you scatter the collected mature larvae on the ground that leaves them vulnerable to the many predators that target insects. It’s fair to assume that only a small percentage of released larvae will survive to become adults. It’s best to keep the mature larvae in a container such as a bucket with a lid to protect them. The container needs to have several holes with a diameter of at least 3/4 inch to allow the emerging adults a way to escape. The holes will also provide necessary air for the pupating BSF and also aid in keeping the temperature regulated. Like the BSF unit, this prepupae container must be completely shaded and protected from rain. Adding an inch of bedding material such as sawdust (not pressure treated), peat, etc to the container will encourage the grubs to pupate, but it must stay dry and loose so the emerging adults can climb to the surface.

If you see dark larvae that seem stiff and aren’t moving do not assume they’re dead. What you’re probably looking at are pupating BSF.

On the linked blog he mentions allowing the mature worms to burrow in soil, so if you have a self-harvesting bucket set up as suggested, just take some of the ones that are in your collector (since they crawled out looking for a place to pupate) and drop them on the ground. Make sure your bucket has a way for adult flies to enter and you should be set.

What I said above about protecting larvae and pupae applies mostly to early in the season when you're growing your colony. Last fall I released a bunch of mature larvae because I thought they had a better chance of surviving the winter if they chose their own pupation site:
http://www.youtube.com/watch?v=4dIc1czSpiI