Using the bulk API means that you are sending your logs making requests directly to Elasticsearch, so you need create an ingest pipeline with the enrich processor.
Then you have two options, pass the ingest pipeline directly on the request, or add the ingest pipeline to your template as the index.default_pipeline or index.final_pipeline.
You can have as many enrich processors you want in your pipeline, the example in the documentation shows how to add a enrich processor in an ingest pipeline.
To add another enrich, you just add another processor to the pipeline, this can be done using a API Request or using the Kibana Interface, which is easier.
To specify a default_pipeline or a final_pipeline in the template, you put in the settings section, the same place where you have the number_of_shards or number_of_replcas.
For example, considering the settings part of a component template, to set the default_pipeline you will need something like this:
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