Salaams… the situation you describe is relatable by many Muslims and may Allah (swt) make it a easy for you
Your question has 2 parts to it:
- attending a burial of a non-Muslim
For the former there is no impediment to offer your condolences or attend because it is part of good manners and high ethics as Allah (swt) says in the Quran, “Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.” 60: 8
- participating in the burial
By participating if this includes an act of worship or reading bible passages, singing a hymn, etc then this is clear cut in Islam that we don’t participate in any acts of worships of non-Muslims be they at birth, life or in death. If by participation you mean attendance or helping the bereaved, as long as this not involve an act of worship it is allowed as stated in the above answer.
There are some who do hold the view that the kuffar are destined to jahannam and so Muslims should not enjoin them in their burials or funerals. Though as mentioned in answer 1 if we want to portray Islam to the non-Muslims who we do live with as neighbours and colleagues then we need a more positive and enlightened attitude.
And Allah (swt) knows best