Using TOR to send your Bitcoin transactions will improve your privacy, but is only one factor.
The main problem with Bitcoin transactions and anonymity is less about whether you used TOR or not when sending the transaction, but rather that Bitcoin transactions themselves are easily traceable. So if you want to improve the privacy of your future transactions, it is recommended to send your coins to a mixer and from there move them to a new wallet (with a whole different set of addresses).
And then, of course, there's Monero. Not as widely accepted, but a good choice for privacy conscious transactions.
This says it all. You can use TOR, but if there's somebody actually trying to trace you they'll simply sit and wait for you to use an exchange or buy something online.
I haven't heard of a case when an institution would try to use IP address to trace the owner of a bitcoin address. It's much easier to trace it back to an exchange, get the buyer's ID and go from there, or wait for it to end up on an exchange and do the same thing. Even if the person they get to isn't you it might be someone related to you or that you've done business with.
Yeah, obviously TOR is only one tool; it doesn't ensure anonymity at all. But between a no-log VPN+TOR to mask your IP address, and Bitcoin services that don't do KYC, you are certainly not low hanging fruit and are likely untraceable, as long as you are careful to continually cycle through new IP addresses and analyze your coins to ensure you've lost the taint.
Smaller services will sometimes send your coins right back to you, so be careful to analyze your own taint if you want to avoid the cost of using mixers. I've always been paranoid of mixers, worried that I'll get back dirtier coins than I put in.
