Using BBMap suite (it will produce some other stats but you can ignore those) :

$ reformat.sh -Xmx2g in=your.bam out=stdout.fa | stats.sh -Xmx2g in=stdin.fa


Could not find sambamba.
Found samtools 1.16
Input is being processed as unpaired
Input:                          9207996 reads           684032432 bases
Output:                         9207996 reads (100.00%)         684032432 bases (100.00%)

Time:                           14.205 seconds.
Reads Processed:       9207k    648.22k reads/sec
Bases Processed:        684m    48.15m bases/sec
A       C       G       T       N       IUPAC   Other   GC      GC_stdev
0.2179  0.2731  0.2738  0.2351  0.0000  0.0000  0.0000  0.5470  0.0632

slow version

 samtools view  in.bam | cut -f 10 | fold -w 1 | awk '($1=="G" || $1=="C") {N++;} END {print (N/(1.0*NR)*100);}'