Driving a led string from batteries
Assuming 28 series leds at 2Vf @ 10mA, then you are looking at 56 V * 0.01 A = .56W.  At 6V, that's 0.56 / 6V = 93 mA. This you already know.

So you have a few options. Multiple batteries in series, or a boost converter Is needed. There are premade modules you can buy for this. Or you can make a primitive one by hand. These are called joule thieves. Often just a ferrite bead, wire and a transistor.

Or buy an led string made for parallel drive.