c-lightning internally calls bitcoin-cli and will pass a couple of commandline arguments to it. These arguments are all prefixed with --bitcoin-* and will match the ones that bitcoin-cli accepts.
So for your use-case you first need to make sure that bitcoin-cli is available on the machine that you will be running the c-lightning instances on. If it isn't you can simply use the Bitcoin PPA to install (but not run) bitcoind which will also install bitcoin-cli (assuming you're using a debian based OS):
sudo add-apt-repository ppa:bitcoin/bitcoin
sudo apt-get update
For a remote bitcoind you need to specify the following arguments:
--bitcoin-rpcconnect=<bitcoind-ip:port> this tells bitcoin-cli to connect to a remote bitcoind instance instead of trying localhost:8332 (make sure bitcoind is configured with -rpcallowip=<ip>, where <ip> is the machine you'll be running c-lightning on)
--bitcoin-rpcuser=<username> the username configured with bitcoind
--bitcoin-rpcpassword=<password> the password configured with bitcoind
In any case I'd suggest running bitcoin-cli --bitcoin-rpcconnect=<bitcoind-ip:port> --bitcoin-rpcuser=<username> --bitcoin-rpcpassword=<password> from the command line on the c-lightning machine to verify that bitcoind and bitcoin-cli are configured correctly.