Remote Management of Bridged Cisco 837

Hello all,
I have a client who has a business DSL connection and has purchased a
Cisco 837 and Pix 506e firewall. Currently I'm planning to setup the
firewall to use PPPoE via the bridged 837 router. So network looks like
this :-

LAN <-> PIX <-> ADSL 837 <-> ISP

The reason why I'm using bridge mode is to allow VPN to terminate on
the Cisco PIX which requires a public IP. The client has only been
assigned 1 IP address for the ADSL connection. I understand that in
order to manage the 837 in bridged mode I need to assign an IP address
on the BVI interface on the 837. I would assume that this IP address
needs to be on the same subnet as the external interface of the PIX
firewall. If that is the case then obviously I would need to have
another public IP address in the subnet as the one already given to my
IP - is this correct? Could I not use a private IP address and assign
one to the PIX as well - not sure if that's possible. Has anyone been
involved in this type of setup? Please advise, thanks.