Hello Minh,
You can enable Auto-RP & BSR (and static RP) on the same router yes. Here’s a quick example:
R1#show ip pim rp mapping
PIM Group-to-RP Mappings
Group(s) 224.0.0.0/4
RP 2.2.2.2 (?), v2v1
Info source: 2.2.2.2 (?), elected via Auto-RP
Uptime: 00:00:23, expires: 00:02:32
RP 4.4.4.4 (?), v2
Info source: 4.4.4.4 (?), via bootstrap, priority 0, holdtime 150
Uptime: 00:02:11, expires: 00:02:11
R2 advertises itself as an RP with Auto-RP, R4 with BSR. R1 seems to prefer Auto-RP.
Interesting to know is that with RP selection, the router prefers RPs that were learned through Auto-RP or BSR over static RPs!
There’s not really a reason to use both Auto-RP and BSR but technically, you could use AutoRP to serve a set of multicast groups and BSR another set of multicast groups.
Running the Auto RP and mapping agent on the same router is no problem, on small networks (and labs) I usually do this.
Rene