[RPG] use a spell with a casting time of “Bonus Action” as the action

The way bonus actions work is:

1. You can't take more than one bonus action per turn
2. If using an ability/spell/whatever is done as a bonus action, you can do it (bearing in mind #1)

So bonus actions aren't something you have or are granted — they are something you do up to a limit of one. Casting the spell is itself doing or taking the bonus action. Anything that is a bonus action means "you can do this on your turn, as a bonus, if you haven't already done some other bonus-type action."

D&D Basic Rules v0.1, page 69 (emphasis mine):

Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action.

You never need something else to give you a bonus action before you can take a bonus action. It is only a description of the type of action it is when you do that thing. It's not a point or expendable that you collect first, and then spend. It's a type of action.

The converse is that if you don't have anything to do this turn that is a bonus action, then you can't take even one bonus action this turn.

So smoke em' if you've got em'!

Controlling a spell is not casting it

On the first turn, you are right, you can cast Spiritual Weapon (as a bonus action) and a Cantrip (as an action) but not any other spell.

On the subsequent turns you can cast any spell as an action and then use your bonus action to control an already existing spell. In fact, you can have both active and control one of them using your bonus action, while the other one is on standby and still cast another spell.

Note, that Bigby's Hand duration is based on Concentration. This means you will not be able to cast any other Concentration spells if you want to keep Bigby's Hand active at the same time. Spiritual Weapon does not suffer from it.