Normal Behaviour
Unfortunately this is pretty normal horse behaviour. Horses are tough on tack and expensive.
Horses will push other horses using many methods and if the other horse doesn't yield, they will escalate to more severe and what we perceive as "violent" behaviours to show the other horse they mean business. There behaviours generally involve biting, kicking or striking. From my experience some horses will be biters and some will be kickers. They will use both, but preference one over the other.
In this case he is biting to pull her into line.
As a more mature gelding he is naturally trying to keep his herd in line. Stallions are the natural herd leaders and geldings retain many of these natural instincts.
When mares are in season, both geldings and mares change in their behaviour. Geldings will often be more interested in mares and mares will often show more interest in geldings, but can also be resistant to the interest from geldings.
When to separate
If he was hunting her to a point of jumping fences, I'd separate them, as there is a risk of injury. I had a young gelding who would continually hunt a young filly around until she was a sweaty mess and there was a risk of injury or her being run through a fence. I kept them separated.
Stability in the paddock
As this behaviour has settled down for your horses I wouldn't recommend separating them. There's a couple of things that will exacerbate this behaviour. If the horses are stalled overnight and turned out each day. The horses will jostle to reassert the herd hierarchy each time they are turned out. Same if they are separated into different paddocks.
If they are maintained in a paddock with the same herd, you'll find this behaviour calms down.
Horses do well with the same herd and not being separated. This way they establish herd hierarchy and don't need to reassert this dominance overtly when first meeting, but rather maintain this hierarchy with more subtle gestures throughout the day, like pushing a horse on.
Introduce an older more dominant gelding
The other way to fix this behaviour is to put a more dominant gelding in the paddock. He will likely keep the younger gelding in line and protect your filly from him, as he will claim her to be his own.