Is Dashing and Attacking in the same turn possible without using a Bonus action? Everything I'm reading indicates a dash takes an entire turn and the entirety of the move.
Fighters can. Action surge means you can use one action to dash, and the other to attack. Using action surge is a feature, and does not require a bonus action.
Outside of that feature...
Bonus actions aside seems to be a weird stipulation to put on this being that that is pretty much the only way you could both dash and attack.
You move on your turn, and you are allowed to take 1 action. (PHB pg. 192). One of those actions could be Dash which gives you additional movement on your turn. Basically you are converting your action into additional movement.
However, you can break up your movement as much as you wish (PHB pg. 190), and can Action during that move (which is an attack in the case you listed). So you can definitely move AND attack, but you cannot dash and attack without using a bonus action to grant either of those things.
Leaving aside spells and class features that allow dashing as a bonus action, the Haste spell would allow a character to use the Attack action and Dash action on the same turn, and a fighter's Action Surge would allow a full Attack action and a Dash action.
A sorcerer could also quicken either Booming Blade or Green Flame Blade to make an attack as a bonus action, leaving their action open for dashing, but I'm not sure if that also violates your premise.