I've seen a lot of other posts here on how to improve BST, from folks much more experienced at the job than I, but one thing as a new BST that drives me nuts is the reuse timer on Bestial Loyalty combined with jug availability.
I get that they don't want us spamming pet (e.g. like SMN) abilities and want there to be a penalty for your 'free' use of a jug, however the 20 minute reuse timer isn't inline with the current state of the game mainly because some of the HQ jugs just are never available as few are crafting them. Those that are available are very expensive (100k-300k per jug), so it isn't something you would want to consume. For me, I have 1 of those I can find and that is it, which means I'm limited to calling one every 20 minutes without running to the mog to reset. That seems a bit unreasonable in todays world of instanced content and adds an unnecessary burden to BST in the party, where they have to go reset JAs just to call their pets.
I feel like either the availability of these jugs needs to be improved (more available via NPC) so Call Beast is viable or the reuse timer needs to be reduced to a reasonable level. A more complicated possibility would be to allow 'learning' the pets and use a single consumable item to call them (which would also solve inventory issues). Given the quantity of jugs available on the AH, I don't think this would impact crafters much at all and it would be a simple change that made the job easier to manage.