pay respects, visit, ask, inquire, question, implore
伺 centers on approaching someone with a respectful or cautious attitude: paying a visit, asking a question, or making an inquiry. The sense of imploring is a more earnest form of asking.
伺 combines 亻 (person) with 司, which likely contributes the sound and the idea of managing or observing. The character suggests a person watching or attending to someone, fitting the meanings of visiting and inquiring.
A person 亻 beside 司 (which can suggest an official or manager). Picture a visitor respectfully approaching an official to ask a question or pay respects.
For シ, imagine a person visiting a shrine (シ sounds like 'shi' in 'shrine') to pay respects and ask for guidance: shrine -> シ.
to call on someone; to call at a place; to pay a visit; to wait on someone
call; visit
call; visit
courtesy call; courtesy visit
to ask for instructions; to ask for someone's opinion; to inquire of
inquiry; enquiry
request form
waiting upon (someone)
inquiring about (one's health)
summer greeting card; inquiry after someone's health in the hot season
to wait and see; to see how the land lies
courtesy call; courtesy visit
asking for instructions; consulting and obtaining approval
informal resignation; unofficial resignation