2.5 and 1 are not old enough to manage their relationship on their own.
Find ways to keep them physically separated when you are not in the room/space with them. Use a Pack-n-play, install a swinging gate in a door, put the older child in a child-proofed room-- whenever you need to take a minute for yourself. So, going to the bathroom? Put baby in the crib to play and put your older girl in a completely separate space.
My rule as a nanny with young children was never to leave them alone together. If I'd had a second child, that would still be my rule.
Your older girl is still getting used to being a person and being a big sister. My guess is that your younger one has recently become mobile and so conflict IS a natural progression. Your toddler is living the toddler creed: everything is "Mine". Thus, she is not viewing little sister as a playmate, but as a threat to her view of everything being 'hers'. This is a very real upset for toddlers, who still process loss in their brains as "pain"-- this triggers her pain receptors and anger, hence, acting out. Little sister sees that this is how we deal with our anger and bites, likely out of some teething pain and some frustration. She's learning that biting makes big sister stop for a moment.
At some point, they are going to forget this. They are going to both be old enough that you can guide them *both*.
One thing I did/suggest during conflict with pre-verbal children is to model a LOT of what you want to see. If you are wanting your toddler to ask the baby when she wants the toy baby is playing with, then I also do that 'for' the baby. When I see the younger, pre-verbal child going after an item the older one has (or getting into their space) I become the 'voice' for that child. "Little sister ask: 'Can I use that toy?" Give your older one a chance to respond, then if it's a 'no' then move on. "Okay, I'll use it later." and then distract/redirect your younger one.
Be this 'voice' for them both as they learn how to check-in with each other when they've hurt each other, or when one or the other needs space/toys, etc. You will be doing this coaching for a LONG time.
One other thing, I have found that toddlers have a very hard time 'sharing' in the "you have it for five minutes, I have it for five minutes" sort of way. I would encourage you to have your child wait until the other one is done using something (clearly done, put it down, doing something else) before offering it to the next child. I have also found that sometimes the older child is receptive to playing in the Pack-n-Play if they have toys they *don't* want to share. Then, the other one can also be redirected, offered other toys, and you can have her play in a different space.
I have quite a few friends who had tough growing-ups with their siblings but are now close. Two sisters I know who had tattled/gotten each other into trouble regularly now are very good friends with each other'; one recently divorced and they now share an apartment and are doing a pilgrimage walk through Europe together this spring. All that to say, fear not. This is only the beginning.:)