Please verify which HRM you own. Of the 4 current Garmin chest strat heart rate monitors being made, only the HRM-Dual broadcasts in Bluetooth. The other three are ANT+ only, and since you don’t have an ANT+ dongle to pick up those signals, your computer won’t see its signal.
Polar H10 ANT + Bluetooth Heart Rate Sensor and Soft Strap::Set the standard for heart rate measurement with the H10 from Polar. Building upon Polar's legacy of heart rate technology, the H10 is set to be the standard for the most consistent and accurate heart rate through the utilization of advanced materials and optimized construction.
As @Tom_Moriarty mentioned I am pretty sure the Garmin HRM Run is ANT+ only. IIRC the only Garmin heart rate monitors that offer Bluetooth are the HRM-Dual and HRM-Pro (which was just released). You can buy an ANT+ dongle for about $10-$20 on Amazon that you can plug in to your computer and it will let you use the HRM-Run you have currently. The Garmin Forerunner 255s Music is the best mid-range running watch with built-in music capability (Image credit: Future) 1. Garmin Forerunner 265. The best running watch for most people
¹When used with HRM-Run™ monitor; included with some models, sold separately on others. ²When used with heart rate. ³Compatible with Bluetooth® Smart Ready phones. Android devices must also use Garmin Connect Mobile app to enable smart notifications. 4 When paired with your compatible Android or Apple device and Garmin Connect Mobile.

Garmin HRM Pro Plus USA: $129.99 $99.99 at Amazon (23% off) UK: £119.99 £97.95 at Amazon (18% off) The HRM Pro Plus superseded the HRM Pro - itself an excellent device - and alongside a couple

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is garmin hrm run bluetooth