I have various machines on my network configured with static IP addresses that are held in DNS. These do not use DHCP. I have a few clients on my network that do use DHCP for IP configuration and have there own hostname set static.

How can I get Bind to amend DNS records for these dynamically allocated IP addresses?

If you are using ISC's DHCPd v3.0, you can configure it to populate a DDNS-enabled BIND zone whenever a DHCP client requests an IP.

In dhcpd.conf:
ddns-domainname "foo.example";
ddns-rev-domainname "in-addr.arpa";
ddns-update-style interim;
ignore client-updates;
key dhcp-server { algorithm hmac-md5; secret "ASDF";}
zone foo.example. { primary 127.0.0.1; key dhcp-server;}
zone 0.168.192.in-addr.arpa. { primary 127.0.0.1; key dhcp-server;}

In named.conf:
zone "foo.example" {
type master;
file "foo.example.zone";
update-policy { grant dhcpd-server wildcard *.nxdomain.com. A TXT;};
};
zone "0.168.192.in-addr.arpa" {
type master;
file "0.168.192.in-addr.arpa.zone";
update-policy { grant dhcpd-server wildcard *.0.168.192.in-addr.arpa. PTR;};
};

See: O'Reilly's DNS & BIND Cookbook