⭐ Merited by vapourminer (1)
If I want to start my own full node, is it better to simply let the client update on its own?
Yes.Quote
Or is there somewhere I could download a trustworthy bootstrap?
Who's crazy enough to share 397 GB compressed data? Wait, that would be me: tmp.loyce.club/bootstrap.tar.gz (this file is scheduled to be deleted in 30 days). This includes blocks and chainstate, both updated until today. I had to figure out parallel compression to speed it up.Code:
sha256sum: 5854df9285ce6eee9083d10c2acd8635bb13f0a588761d3edcb267c062c5a1ea
Quote
Would the bootstrap save any time in downloading?
Maybe, maybe not. It would be cool if you try both, and answer this question once and for all 
Do not download the blockchain from a 3rd party that goes against the principle of having a full node.
You can (and should) have your own Bitcoin Core verify all blocks again. That undoes any potential time savings from downloading the bootstrap 