The Clarets are currently riding high in the Sky Bet Championship and have a 10-point gap in the race for automatic promotion with just 10 games to go.
They have turned to Northern Ireland international Baird, most recently of Reading, to provide some vital experience down the season's stretch.
The 32-year-old can play in defence or midfield and may occupy the right-back spot at Charlton this weekend with Kieran Trippier a major injury doubt.
"He's very experienced and can cover three or four slots," said Dyche.
"In a small squad like ours players like him are who've been thinking about.
"He's played Premier League football on a regular basis and international football.
"That experience can be very useful on any given occasion. We've checked him out, made sure he's fit and well. If he's feeling well and he's right, we'd use him accordingly."