To get apt working, just follow this part on the wiki and then SSH into the BashBunny using PuTTy or KiTTy with IP 172.16.64.1
Works for me, as you can see:
root@bunny:~# ping 8.8.8.8
PING 8.8.8.8 (8.8.8.8) 56(84) bytes of data.
64 bytes from 8.8.8.8: icmp_seq=1 ttl=45 time=18.4 ms
64 bytes from 8.8.8.8: icmp_seq=2 ttl=45 time=14.9 ms
64 bytes from 8.8.8.8: icmp_seq=3 ttl=45 time=18.2 ms
^C
--- 8.8.8.8 ping statistics ---
3 packets transmitted, 3 received, 0% packet loss, time 2002ms
rtt min/avg/max/mdev = 14.949/17.190/18.419/1.587 ms
root@bunny:~# apt-get update
Ign http://httpredir.debian.org jessie InRelease
Hit http://httpredir.debian.org jessie Release.gpg
Hit http://httpredir.debian.org jessie Release
Hit http://httpredir.debian.org jessie/main armhf Packages
Hit http://httpredir.debian.org jessie/main Translation-en
Reading package lists... Done
root@bunny:~#