Multi class spell slots

So I'm playing a Bard and wanted to multiclass into warlock to get it's spells and invocations but I know that warlocks have special slots for their spells. What I'm wondering is if I'm supposed to be able to cast my Bard spells using the pact slots and the other way around?

You can, yes. The Multiclassing rules have a note on Pact Magic saying as much. However, Pact Magic slots don't stack with Spellcasting slots in the Spell Slots at Higher Levels chart.

Worth noting “Bard slots” aren’t a thing in 5e; any slots other than Pact Slots go into a general pool per the multiclassing table and aren’t attributed to a particular class.