Describe recurrence rather than one isolated sighting
Note the rooms or entrances affected, whether webs repeatedly return and any other insects nearby. A photograph may help identification if already available. Do not handle an unfamiliar spider to get one.
Set a realistic service scope
Ask which areas need checking and whether practical changes around access or other insect activity are relevant. A completely spider-free property is not a realistic guarantee. The proposal should describe what the service intends to address.
Does every spider need treatment?
A single sighting does not by itself establish a need for treatment. Discuss the pattern, location and concern before choosing work.