That price is fine. Be sure to use an acid in your cleaning solution. It will help to set the dyes so that you don't have any additional bleeding. Be careful not to get the rug too wet. I would suggest a spray and extract. Be sure to extract thoroughly and dry it with blowers.
I would take into consideration what YOU are comfortable doing. Offer the client a few options based on that. If you feel that you cannot get it to an acceptable level, send it out to someone that you are comfortable with. Personally, I would just wash it(on our wash floor).
Every rug shop should have multiple options for handling all types of textiles. Full submersion, low-moisture/encapsulation, dry absorbent compounds, dry cleaning, etc. It takes a lot of rugs and clients with differing expectations and pocketbooks to really know how and when to offer which service. Stick to what you know until you master many methods. Rugs are so diverse, you should be too!
Im not an expert on these, but I remember reading that the old machines had 3' looms, so these would be made in sections and sewn together. This is why carpets have been priced the square yard. Although these have very little resale value, they can have a lot of sentimental value from being handed down from the gradmother.