Basic Setup of F5

i thought bridge mode you said is something like this.

4 Installing a BIG-IP System without Changing the IP Network

http://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/ltm_implementation/sol_vlans.html

as looking at your diagram, i think routed mode is more sense.

In routed mode, if VIP sits on the external VLAN range, i understand it but if its sits directly on internet IP which is not part of external VLAN range, then is it a normal deployment design suggested by F5? i am sorry i might not catch you. anyway, what i want to say is virtual server is able to be listening on any ip range on any vlan. definitely, you are able to enable virtual server on specific vlan.

e.g.

[root@B3600-R66-S41:Active] config  tmsh list ltm virtual bar
ltm virtual bar {
    destination 2.2.2.10:http
    ip-protocol tcp
    mask 255.255.255.255
    pool foo
    profiles {
        http { }
        tcp { }
    }
    vlans {
        external
    }
    vlans-enabled
}

if traffic is able to reach virtual server, it is fine. for example, you may have virtual server listening on 3.3.3.3:80 (which does not belong to any vlan) on internal vlan. if client on internal vlan sends request to 3.3.3.3:80 and it can reach bigip (for example, client's default gateway is bigip), bigip will load balance it.