Which Debian release are you using?
Are you bridging to a WiFi network on your Mac or a wired Ethernet network?
Is the Network Adapter in the VM's sessions configured for bridging to Autodetect, WiFi or Ethernet?
Are you connecting to an access point or wired network that refuses to hand out more than 1 IP address to a MAC address?
I'm assuming you are using DHCP in your Debian VM. If you configure a static IP address instead of using DHCP in your Debian VM, can you access the network?
Are you bridging to an network that is configured as a VLAN?