Not in my opinion
Bardic inspiration, unless you are taking multiple levels of Bard, will only ever be up to 5 times per long rest, that is less than once per fight if you have the intended number each day, and even less if you also use them out of combat.
So this option won't give you something to do every combat, if that is your requirement.
Warlocks are balanced around the Hex spell (which really should be a class ability in my eyes), which is not only a bonus action to cast, but a bonus action to switch targets whenever you make a kill. If you target carefully you could be doing this quite often (which works well as a fiend warlock with your Dark One's Blessing), so is a high incentive to look to finish off the weak(ened) targets.
From a Hex perspective, the usual choice for a Warlock in combat is "do I cast Hex in this fight or not?", because Hex uses your concentration, and at high levels lasts pretty much the entire adventuring day, so the idea is that you cast Hex once at the beginning of the day, maintain concentration on it and use the other slots for other things.
What are some other options?
It seems to me that you like to use a bonus action every turn, and for a caster class this is pretty rare outside of certain spells like Spiritual Weapon. I have had a quick look through the Warlock spell list, and none of the usual bonus action spells are on the list. I presume this is for balance reasons. So sticking with Warlock leaves you saving your bonus action to move Hex.
I can't list every option here, but the obvious options are Bard and Sorcerer.
Bard you will get additional bonus actions when you reach level 3 and get 2nd level spells, but these will all compete with Hex for your concentration slot - Heat Metal stands out here. Between the spells and bardic inspiration you will have more bonus actions, but there is a cost against your Warlock levels.
Sorcerer gives similar issues, you will be able to get meta-magic to quicken a few spells, and also get spells like Dust Devil, but again this takes concentration so conflicts with Hex (it is also a poor spell).
So basically either option will give you a few bonus action options, but they won't be around every combat, let alone every round, unless you invest a good number of levels. Personally I would stick with Warlock.
If you do stick with Warlock you will eventually get a single 7th level spell, that can be used on Crown of Stars, which for a full combat will give a very good use of your bonus action, but that is far in the future.