I was amazed to learn that indeed, if you get a (NON-money) property gift from another US person, indeed you "GET" the capital gains tax!
"when you give away your property, the tax basis (or the original cost) of the property for the giver becomes the tax basis for the recipient"
It would seem that in general, a gift from someone overseas is wholly non-taxable to you in the US
ASIDE: note that YOU MUST REPORT IT or you will be fined 25% of the amount.
If it is a "US - Situs" item, they will f' you. Here's a gem:
"Danger: It is not recommended that an offshore relative wire funds directly into your U.S. accounts. There is a risk the IRS or state tax authority could argue that for the millisecond that the transfer bounced around in U.S. Cyberspace the government had in rem jurisdiction and assert a transfer tax."
Based on that opinion-piece for a tax practice, it's entirely possible that the US will/has declared that bitcoin is US Situs (since almost all bc processing is on US hardware - anyway, they could just declare it); if so you're screwed, it would be like your foreign relative giving you a house which is in the US which she owns.
Would it be worth it for Russian Aunty to simply change it to dollars, and then gift you the dollars? You can then buy bc if you like, or whatever. If it's a dollar gift you are home free.