Is it permissible to allow a male or female non-Muslim to sit in my place on the bus if they do not find a seat?

It is permissible to show kindness and benevolence to a non-belligerent disbeliever. This includes standing up for him to sit down if he is in need of it due to old age or illness. In fact, it might even be recommended, and the one who performs it will be rewarded if he intends thereby to invite the person to Islam by demonstrating its tolerance and the good character of its adherents. This is based on the Almighty's saying: ﴿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.﴾ [Al-Mumtahanah: 8], and the Prophet, peace and blessings be upon him, said: "In every living being with a moist liver there is a reward."