oh surely you'd be able to
the best way is to run the official Bitcoin Core, it is a bit massive and something most users won't want to do, with that you become a full node, you sync the whole blockchain to you, with this you'll be directly connected, your wallet would be local on your pc and no intermediaries
https://bitcoin.org/en/bitcoin-core/
there are other options that work as a middle ground to have your wallet local without running a full node, run one of these wallet software on your pc, encrypt, backup, etc, less effort than with Bitcoin Core but still not as easy as coinbase/circle/neteller/paypal
http://www.bitcoinarmory.com/
https://electrum.org/#home
it all depends how how complex and private a setup you want to have, if all you want is to put up a couple of hundred bucks a few times a year i don't know how willing you are to make this extra effort, remember revolutions die because revolutionaries grow tired and old