Well , you should share your network design , or at least what are network devices that locate in front of BIG-IP.
>> you can access this Virtual server through internal network with Virtual server Private IP and this is fine. >> I will assume that you have Firewall in front of Bigip and facing internet ( Public Range of IPs ). So you need to follow the below steps :
you need to assign a public ip for this Virtual server through Firewall , let's say " 100.100.100.100 ".
you will perform Destination NAT , and Map this Public IP to Virtual server Ip " Private " let's say "192.168.1.10".
I communicated with internal team regarding this issue, they was saying all configuration on firewall such as NAT and assign public IP for this VS has been done please check on F5 configration now I wont know how check the traffic hilts on VS and advice if any any configration it must modify it , check the aatched if need any modfiy it