When do Spider's prices reset?

Solution 1:

According to this article, the price for the Masterwork Core doubles with each purchase (as you have already seen). While this will make the Masterwork Cores expensive if you continually buy them, the price will reset on a daily basis rather than a weekly basis.

The easiest way to get Masterwork Cores is from new vendor Spider. You can buy them for Leendary Shards, but the cost doubles for each purchase on the same day. The first piece you can get for 10 Legendary Shards, the second one for 20 Shards, third for 40 shards, and so on. The great news is that the price resets daily.
_{(emphasis my own)}

The article does not state an exact time the price resets, but based on this Bungie article, the reset would occur around

Pacific Daylight Time (PDT) Reset will be at 10:00 AM Pacific (1700 UTC) while Daylight Saving Time is active from March to November.

Pacific Standard Time (PST) Reset will be at 9:00 AM Pacific (1700 UTC) while Daylight Saving Time is inactive from November to March.