Forgive me if this has already been asked, but I've been through pages of searching various combinations of "attack", "touch", "spell", "melee", "bite", "weapon", and a few others.
Most touch spells call out "Make a melee spell attack", and I get that an action can be "Cast a spell" OR "Make an attack" so you can't stack them.
But in the spell Bestow Curse, it simply says, "You touch a creature…"; nothing about being an attack. Specifically, the spell is a WIS save.
So my question is, could my Lizardfolk Cleric deliver this touch via his teeth sinking into tasty flesh? Yes, he would need to make an attack roll for the bite, but the victim would also need to make a WIS save to shrug off the curse.
I'm not saying all touch spells across the board can be done this way, just touch that don't require an attack.
Related, but not the same:
Best Answer
Not in the same action
Attacking a creature is an Action. Bestow curse, the example you linked, also requires an Action to cast. Your character cannot do both at once.1
This is a matter of adhering to the action economy in this edition of the game.
As flavour
Absolutely! If you have haste, or spread it out over two turns and it makes sense, casting a spell through teeth sunk into flesh is a really fun idea! A spell with touch range and no melee attack is effectively a spell with 5ft range (on a grid). All you need to do to cast the spell is to be adjacent.
1If you had multiclassed as a Fighter, and have the Action Surge feature, you could take two Actions in the same round.