Your bridgesii will be fine outside overnight in the summer. Just put it outside when the risk of frost is past - and if there's an unexpected cold snap, wrap it up in a thick blanket. Save the lighting tent for early spring and late autumn if you want to stretch your growing season. In winter, keep dry and protect from frost.
Taking your cactus outside only when the weather's sunny puts it at risk of sunburn.
Be careful when using fertilizer on your cactus. During the active growing phase it will respond well to tomato feed - diluted to half strength - every couple of weeks, at least once the bonemeal is depleted. It sounds like your compost mix wouldn't need additional perlite, considering it was a cactus mix in the first place. If you wanted to add something to improve drainage, I'd suggest lava chippings.
Once your cactus gets established you won't want to be carrying it around every day - and if you get a collection started you'll soon be thinking of moving somewhere where the cacti can stay outside as much as possible! Best wait until you at least have a few window sills at your disposal before expanding your collection.
“There is a way of manipulating matter and energy so as to produce what modern scientists call 'a field of force'. The field acts on the observer and puts him in a privileged position vis-à-vis the universe. From this position he has access to the realities which are ordinarily hidden from us by time and space, matter and energy. This is what we call the Great Work."
― Jacques Bergier, quoting Fulcanelli