[mothered]

I successfully EB'd a pair of Bose earbuds from Currys and sold them on Facebook marketplace yesterday

Did you use your real credentials to buy & sell?

the buyer has just messaged me saying they aren't connecting to the app,

It could be due to a number of reasons.

Ask him/her to explain the Issue.

and is asking me for a receipt.

Say that you've received them as a gift.

Is it possible that Bose have blocked that serial number from connecting to the app?

As with Sony, they have the capacity to blacklist the serial number.