For Ant+:
One simple option is probably a Raspberry Pi, Ant+ USB stick and this python library and example:
The library is a bit of a mess from what I remember, but it did work for the most part. The example is a bit cryptic unless you are familiar with Ant+ specs. If you want to delve deep into ant+ world, all the specs can be found from https://www.thisisant.com/ you just have to register and accept a bunch of slightly disturbing license agreements.
For BLE:
A new Raspberry Pi with BLE support and implementing something using the bluez stack might work? I haven’t tried it but there are some examples like this behind google:
For truly embedded Ant+/BLE development I’ve personally done some fun projects using NRF52832 chips. Plenty of examples for connecting to and pretending to be various BLE/Ant+ HR devices. The chip doesn’t have wifi/ethernet though so it doesn’t suit your needs of being able to push stuff to MQTT.