WHOOHOO WISHES~
This week Bakura will have his (mod-approved) shadow magic back. Now because he doesn't have the Ring he's not at full strength by any means, but he can still do a number of shiny tricks. I've broken them down into different sections here to help explain them and to outline the strength levels and restrictions. I've done my best to base them off logical extrapolations from the abilities he's seen using in canon, but if you have any questions about anything here, don't hesitate to ask!
Manipulation of ShadowsThis is exactly what it sounds like, being able to "grab" shadows and use them. This is based off his ability to summon a "playing field" in the Shadow Realm. Obviously he won't be able to duplicate that in Facility with the collars, but he's able to summon enough to create a shield for himself if he was being attacked and enough to "throw" shadows at someone as an attack.
IllusionsThis one is really where Bakura's talents are going to shine -- the ability to create illusions that look, feel and sound completely real. Only a magical or otherwise non-standard sense would give them away, and even then they will still play upon emotions. People, objects, locations... anything that Bakura knows or can find out enough about to reproduce. It's all in the person's head, but it's damn believable. Outwardly, the person probably looks like they're in a trance.
SummoningOne of Bakura's powers granted by the Ring was summoning Duel Monsters onto the physical plane.
However that's no so different than summoning
kaa monsters, which he was doing without the Items. So I've tried to strike a balance in deciding that, with effort, Bakura could use magic and trap cards, but not summon any actual monsters while in Facility. (At least not outside F3 and uncollared.) What's a magic and/or trap card? A good example would be
Trap Hole: while in Duel Monsters it would destroy an opposing monster, when summoned "for real" it would literally just create a hole for someone to fall into.