You may do Realtime PCR using primers for 'origin of replication site, i.e., replicon typing, there are PCR primers already available for plasmids of different compatibility groups with multiplexing ability.
Counting number of bands may be misleading as a single plasmid in different stages of supercoiling may give multiple bands.
You could determine the number of different plasmids carried by a bacterial isolate using a number of techniques depending on the nature of your isolate and the plasmids. If the plasmids are reasonably small and high copy number, then DNA samples can be assessed by gel electrophoresis. In order not to be confused by plasmid supercoiling you could try digesting the DNA sample with restriction enzymes likely to cut only once. However, if you had many different plasmids each with multiple cut sites, the banding profile will look very complex. You could attempt to obtain a draft genomic sequence using a NGS technique, but this approach is expensive and plasmid DNA may to be well-represented in the total DNA sample. As suggested by Bhoj R Singh, you could try a PCR approach targeting known plasmid replication, maintenance or transfer functions, and use theses as a measure of the number of different plasmids present. However, there are a lot of examples of plasmids having multiple replicons etc. which will confuse the issue.
As you are looking at antibiotic resistances, have you considered transforming or conjugating another host bacteria with your isolates? It may be possible to determine how many plasmids there are based on the diversity of transformants or transconjugates you can recover. This will also mean that you have isolated single plasmids in your host which would mean that subsequent analysis is easier. However, this approach requires that you have a host bacterium that is phylogenetically close to your isolates, as transformation, conjugation, plasmid replication and maintenance are all sensitive to host range issues.