It would of been nice if the bank let you deposit items for a fee. But really there is no need. Ruby chest all reset on going back to the first day. And there are several ruby chest in the field and in town if you know where to look.
If you're talking about the bomb bag, you keep it. It's only the bombs that disappear but if you have the bag they'll occasionally drop from enemies and bushes.
As chartube12 said, you can also loot the silver rupee chest in termina on every "reset", play the lottery once you found the numbers of the first day, etc. to get some cash for items.
There's a chest with a Silver Rupee (100 rupees) in East clock town, go near the observatory entrance, follow the path to the right you'll see a small gap that you gotta jump across, keep following that path (past the Darling and Honey shop) and you'll get to it, good this is it resets each time you go back in time, so you can farm rupees there easilly.
There's also a second chest when you get past the bomber kid blocking your way (area leading to the observatory). Once you get past the kid instead of going right, go left, there's a bit of water and a small place you can stand (past the skulltula), you'll see a cracked wall, blow it up with a bomb and the chest in there has another silver rupee.
What I do after using Song of Time is put on the Goron Mask and roll around Termina Field a couple times, hitting all the grass I can see. That fills up my arrows and bombs pretty quickly. Plus, it's fun!
There is also the Blast Mask which can be used in place of regular bombs in many cases.
Just get the most useful mask in the game, the Blast Mask, by waiting around in North Clock Town until midnight on day 1. Sakon will rob the Bomb Shop Lady, cut that jerk to save her goods and you'll be rewarded with the blast mask, which is basically an infinite bomb. Put it on, hold R and explode without taking damage!