Yes, the bitcoin is a very safe method for payments, plus its also fast.
The only thing you need is a secured wallet, use blockchain or something.
I definitely know that bitcoins are safe.
In particular, because I think a lot of people use it. But I think the online wallets are less safe indeed.
Safety is upto How you are maintaining the privacy policies at there. Just are feel safe in online wallet, check it on your two factor authentication or try offline wallet or cold storage.
For my case bitcoin is safer than the fiat currencies. Which is aware that much and which handy take more money with in mobile or other device itself.