The basic principle is that the Muslim woman should not go out of her house except in cases of necessity. If there is no need for her to go out then she is enjoined to stay in her house as Allaah says (interpretation of the meaning):
“And stay in your houses, and do not display yourselves like that of the times of ignorance”
Ibn Katheer (may Allaah have mercy on him) said:
This etiquette is something that Allaah enjoined upon the wives of His Prophet (peace and blessings of Allaah be upon him) and the women of the ummah follow them in that.
Tafseer al-Qur’aan il-‘Azeem (3/482).
If a woman needs to go out, then she may go out subject to the conditions decreed by sharee’ah, such as wearing proper hijab, and not wearing perfume and adornments, but if she goes the distance that is regarded as travelling then she must have a mahram with her.
If a woman is overweight, obese or sick and needs a man to help her get on or off the bus, in that case it is not permissible for her to go out except with a mahram or a woman who can help her with that. It is not permissible for a woman to allow a man to hold her hand or touch her because he is a stranger (non-mahram) to her.
For details on the ruling on touching a non-mahram woman, please see the answer to question no. 21183.
If a woman is compelled to go out and she does not have any mahram who can help her get in and out of the bus, then she can ask one of the women on the bus for help.
If she cannot do any of these things, it is permissible for her to ask a man for help, because cases of necessity make forbidden things permissible, but necessity should not be exaggerated. The shar’i principle that is well known among the scholars is: “Hardship brings ease.”
It is worth noting that these circumstances that you are facing do not make that which is forbidden permissible, rather it remains haraam until the Day of Resurrection. This is in general terms, but a concession may be allowed in cases of necessity and at times of need only.
If the need ceases to apply, or it is possible to deal with it in a shar’i manner, such as seeking the help of a mahram or another woman, then the original ruling, that it is haraam and a sin, comes into effect again. So beware of persisting in it.
And Allaah knows best.