The unintuitive thing to remember about low data rate applications is that the most energy expensive operation is keeping the receiver turned on, as opposed to transmitting a packet. So everything hinges on keeping the receiver turned on for the shortest amount of time possible. Bluetooth LE achieves this by establishing a schedule between the host and the device, and the device will turn on its receiver according to the schedule, receive a message from the host, and respond with an acknowledgement or data.
The important criterion is not so much how often you need to send data, but what the acceptable latency is, as that determines the "connection interval".
A Bluetooth LE link in connected state (the schedule has been established) can be very low power and could be a good option for your application. You can try out this calculator:
https://devzone.nordicsemi.com/power/I would consider the NRF52 line of chips (or one of the myriad modules based on it) a good choice for that application as it can act as both host and device, and the chips and SDKs and support are really good. It's still a fair bit of development effort to build the host and device parts but there are examples for both.
The HC06 line is not suitable as it's traditional Bluetooth, not LE.