I want to connect my database to CRM and as far as I understand BizTalk is the best choice. I know that BizTalk has its own messaging system, but is it enough considering the stability of my data or shall I put a message-bus in between?
Adding another link in a chain will not make the chain more available.
BizTalk has many built in mechanisms to improve the stablity of this connection. Think of automatic retries, automatic throttling. There is no need for servicebus for stability.
You may want to use servicebus when you need to use a protocol that BizTalk does not support (for example, CRM in the cloud uses azure queues, which BizTalk 2010 does not support (higher versions do)).
If the environment that you run BizTalk on is stable, then BizTalk will be stable as well. If the environment is not-so stable, then you can look into clustering to create some added stability.