Send/fetch baby from infant care alone with work bag

Hi working mummies that send their baby to infant care, if you’re sending or fetching them alone and taking public transport and not using strollers, what kind of bag do you use for you work? As you need to carry baby in carrier or by hand, carry his diaper bag and also your own work bag. My maternity leave is ending soon and im still figuring out how to go about this. I wont be using stroller as it’s a hassle especially when im alone and need to rush.