You can check out examples from Apache Karaf github repository to see how bundles for OSGi applications are structured there. Christian Schneider has also done talk about OSGi best practices and has some examples in his repository as well.
Generally you want to keep your bundles small with least amount of dependencies as possible. Due to this I would recommend having only one integration per bundle. This makes installing integrations and their dependencies easier and offers some flexibility if you ever decide to split integrations between multiple Karaf instances.
For connectivity stuff your best bet is usually to use/create/publish OSGi services. For example with pax-jdbc-config you can use config files to create new DataSource type services which you can then use to connect to different databases from your integration bundles.
Publishing own custom services is pretty easy with declarative services and could easily be used to share connections to internal systems, blob storages, data access objects, etc while maintaining loose coupling by keeping actual implementations hidden with interfaces. For services the recommended approach is to have separate API and implementation bundle so bundles that use the service can just add dependency to the API bundle.
For deployment you can create your own custom Karaf distribution with bundles pre-installed, deploy bundles using Karaf features or use the hot deploy folder. For the two latter ones you might want to configure Karaf to use external folder for bundle configurations and hot deploy as process of updating Karaf is basically replacing it with new installation.
[Edit]
If we have 50+ transformations and put each in its own bundle, then I would have more than 50 bundles to manage. This is just a single instance. Other customers would have their own instances, again running 50+, 100+ bundles
Would say that the key thing here is to try to simplify and identify repetition in bundles. Often these can be converted to something more generic and re-usable.
With OSGi you can use Declarative services and OSGiDefaultCamelContext to instantiate Camel integration instances per configuration file which can be useful if you have multiple integrations that work pretty much the same but only have minor variations. Don't know if camel has support for this with blueprints.
With many bundles efficient use of Karaf features or OSGi features (R8) can be vital for handling the added complexity. Features make it considerably easier to install and update OSGi applications which consist from multiple bundles, configuration files and other features.
Still there's really no rule on how big is too big for single OSGi bundle. Grouping closely related things in to single bundle can make a lot of sense and help avoid splintering things too much.