Spiritual Weapon attacks using Bonus action: it is not an Action
Bonus Actions and Actions are not interchangeable in Combat.
Bonus actions don't become Actions
Does this mean that you get a bonus action on a bonus action, or does the first bonus action become an action?
Neither. It does not become an Action, and you do not get a Bonus action on a Bonus action. One bonus action per turn.
From the spell description, you cast spiritual weapon with a Bonus action on round 1. You can attack with it on round 1 as part of the casting.
You can take some other Action during your turn on round 1 as well as using that bonus action to cast that spell. For example, you can Dash, Shove, Disengage, Dodge, Attack (with something else).
You attack with spiritual weapon on rounds 2 through 10 (and move it as needed) as a Bonus action; you use your Action to do another thing, as before.
Actions and bonus actions aren’t interchangeable1. (Sage Advice Compendium, p. 9)
A Bonus action1 is its own thing in D&D 5e, and is separate from Actions. (CH-9, PHB). It is treated separately from Actions (capital A) but is a kind of action (small a). Yes, it can be confusing.
What can a creature do during a round, and during their turn?
During a round a creature can take an Action, Move, take a Bonus action (if it has one) and Interact with an Object on their turn. They can use a Reaction on another creature's turn if something triggers a Reaction. (PHB, p. 189-190)
How does spiritual weapon work?
I will illustrate by using five rounds of Combat. A Cleric (level 3, Str 14, Wis 16, Con 14)) versus a Bandit Captain (BC). Initiative roll for Cleric is 11, for BC is 10. Cleric goes first.
Cleric. Take the Dodge action and Moves to within the spell's range of the BC. Casts spiritual weapon as a Bonus action; makes an attack. Rolls 5, misses.
BC. Moves to melee range, has no Bonus action, attacks Cleric. Rolls 18, 17, and 9. (Attacks are with disadvantage due to Cleric Dodge) Rolls second d20's of 10, 8, and 20 respectively. Cleric's AC is 16. All miss.
Cleric. Casts guidance (Action); with Bonus action attacks BC with spiritual weapon. Rolls 15, hits for 1d8+3 force damage. (Roll 4, 7 damage).
BC. Attacks cleric, rolls a 17, 10(Scimitar) and 12(Dagger). Does 11 damage total. (Cleric has 14 Con / 24 HP). Cleric makes a concentration save for guidance but not for spiritual weapon. Rolls 12. Concentration is not interrupted. If she had missed that save, guidance would end but spiritual weapon remains active.
Cleric. Shoves BC (Action) to knock it prone. Strength of 14 (+2); proficiency Athletics (Sailor background) +2 and adds 1d4 from guidance: rolls a 3. Rolls an 11 on the d20 shove attempt; results is 18. BC rolls 11, adds Strength bonus (+2), Athletics (+4) makes 17; BC knocked prone. Cleric uses Bonus action, attacks with advantage (spiritual weapon). Rolls are 5 and a 14. Hit. Roll of 4 (1d8+3) yields 7 more damage. Moves back 30 feet; provokes opportunity attack(OA) from BC, who is prone; OA with disadvantage. Rolls 19 and 7. Misses.
BC. Gets up (uses half of its movement) pursues the Cleric but it can't reach her as only 15's of movement remains. Throws two daggers. Rolls an 11 and 13. Both hit, 10 points of damage. Cleric is in trouble(has 3 HP left), but does not need to make a concentration check on spiritual weapon.
Cleric. Casts Hold Person. (DC Wisdom save 13). BC Rolls 12. Wis mod of 0. Fails. BC is paralyzed. Cleric moves next to BC, uses a Bonus action to attack with spiritual weapon (with advantage, due paralyzed BC). Rolls a 2 and a 13, hits (Automatic critical hit due paralyzed). Rolls 2d8+3; 9 force damage.
BC. Unless he makes a saving throw on its next turn, and turns subsequent, can't move or attack. BC misses save (Rolls 11).
Cleric can attack with mace or a spell (Attack action), and with spiritual weapon on the following turns (with advantage). Concentration is used for hold person, not for spiritual weapon. She could take the Dodge action (in case the BC makes a save) and still attack using the spiritual weapon (Bonus action). But instead ...
Cleric tries a nova-type attack. Drops her mace, casts inflict wounds(touch) to attack (with advantage). Rolls 4 and 10. +2 for spell proficiency, and +3 for Wisdom - 15 hits AC 15. She does 3d10, and another 3d10 (critical hit) so rolls 6d10 for 33 damage. (BC still alive!) Uses Bonus action to attack with spiritual weapon rolling 1 and an 11. Hits, 2d8+3 damage, rolls 9 (+3) for 12 force damage. Finally kills BC (who had 65 HP to start with).
Spiritual weapon allows for a lot of combinations on rounds 2-10.
The point of the above illustration is to show how the spiritual weapon, once created with a Bonus action, can be used with the same Bonus action to attack, and to attack on subsequent turns in combination with a variety of other Actions. The Cleric never needs to make a concentration check for spiritual weapon.
Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. (p. 189)... You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take.