If I want to start my own full node, is it better to simply let the client update on its own? Or is there somewhere I could download a trustworthy bootstrap? Would the bootstrap save any time in downloading?
Do not download the blockchain from a 3rd party that goes against the principle of having a full node. If you want to run a node you want to make sure you download the blockchain from the source and it verifies correctly because if you download it from a 3rd part they could have altered the blockchain without you knowing. It should not verify and should show a error but I would not risk downloading it. I doubt it would save a lot of time downloading the blockchain is quicker then it was many years ago it mostly gets slow when you have poor hardware or internet connection.