So I was wrong (it's still there) but I was right (it's no longer a combat buff)?
Those spells are still there, yes, but they go against bounded accuracy concepts following previous versions so 5e has them modified to a more appropriate format. They are more for non-combat benefits and still have some combat application even so. Cat's grace, for example, would provide advantage on initiative so going first becomes a combat benefit.
Bards did not get any overboard treatment, BTW; full caster progression replacing 3e song abilities is largely a wash. Full caster and magical secrets are over-estimated in value. Bards don't even have much in the way of buffing outside of BI dice unless they add it via magical secrets. I would still look at clerics and paladins for buffs.
Stacking buffs aren't as possible (can still be done with multiple casters) but it's also not so necessary because of bounded accuracy. A cleric can go with a more combat oriented domain, heavy armor and shield, the bonus damage applied at 8th and 14th levels, and one buff or area spell limited by concentration to continue with the same general feel the 3.5 buffed out clerics had. Spiritual guardians was mentioned as a popular choice, as well as bless, but there are more options.