You are wrong about how people will react

The consistent finding is that people underestimate how willing others are to help — by a wide margin, in every setting it has been examined. The imagined reaction is irritation or a lowered opinion. The actual reaction is usually mild pleasure at being asked, because being useful and being trusted both feel good.

Which means the cost you are weighing is largely imaginary, while the cost of not asking is real: time lost, work done badly, a problem that grows. That asymmetry is worth knowing about before the next time you decide not to bother somebody.