Indian SIM cards (Jio, Airtel, Vi) generally only work in a small radius around the border. Further inside Bhutan they're unreliable, and expensive if international roaming is enabled.
Bhutan has two mobile operators: Bhutan Telecom (state-run) and TashiCell (private). A tourist SIM is inexpensive, commonly cited around Nu 210 including some talk-time and roughly 1 GB of 4G data, valid for about a month. You can usually buy one with a copy of your passport or ID. Wi-Fi is generally available in hotels in the main towns, but less reliable in remote areas.