Adapt your game sessions a bit to the players, since it's a small group
My question is, however, would this make a good party?
TL;DR: yes, Cleric, Bard, Warlock is an OK set up
Three points that I recommend you reconsider before you start.
Author and plot
Player class change before play starts
Perceptions on bards and clerics
But first: Party size
The game's basic design is a four character party, though I've seen "three to five" as a nominal basic party size tossed around. I've played with three quite a bit, and with five. The difference during an encounter is noticeable. If your players are not optimization driven, the action economy can get a three player party into trouble quickly, particularly when the dice swing against them. If you are heavily into exploration and social encounters, it won't matter as much and each player gets more spotlight.
Author with a plot - proceed with caution
If your players don't mind a bit of railroad riding to keep the game moving, that's fine, but be aware that it is the players' decisions and choices, and those consequences, that drive their fun. Even if you have certain nodes and BBEG's to overcome (the opposing forces in the game world) trying to get the players to fit into your plot can create problems.
Class choice is up to the player - let that be their challenge
I've spoken to my Tabaxi Bard, and she's open to changing her class, as she doesn't really know whether or not she likes D&D yet, but I also don't want to make decisions for her.
New players are confronted with the tyranny of choice. They are the kid in a candy story with only enough money for one candy bar. The use of NPCs, or hired guards/specialists, is one way that you as the DM can offer the players an option of getting the help they need from the game world to overcome various challenges.
This approach is modular: as each challenge or situation arises, they
may need to seek different kinds of assistance or specialists. It
can also open up a lot of fun role play opportunities when the PCs
negotiate for services and access specialists, or as they negotiate
for/appeal for assistance from various NPCs in the game world. The
latter process can help them feel that your game world has more depth
as they form relationships with NPCs by doing that.
For new players, leave class change options open: if after a few sessions they find that they are not happy with their character class let them swap to a different one. In official play, they allow this in Adventurer's League up to fifth level.
Keep that option open in case you need it, particularly for new players.
- Experience. Even experienced players may want to change PC class. I am in a tier 3 group (all PCs are currently between level 12-15). Two of the players (since I joined the group well over a year ago) have let go of a 12th, and a 13th, level character and begun a different character at 11. They join the group during
the adventure. One of them dropped a wizard to roll up a ranger. It's going fine.
"Bards and Clerics are more like healers" assumption
Not so fast. My Tempest domain cleric in our first campaign was a front liner. So too was my original Life domain cleric (who died) - RIP Korvin Starmast. Bards have a wide variety of ways to contribute to a party. Drop a few of your assumptions and Let The Players Play. Let them find out how to get the best synergy out of their character skills and features within their little team. That's part of the fun.
The Lore Bard can start with some key skills that are usually used by Rogues; (thieves tools, stealth, persuasion, deception, acrobatics). In a small party, having a bard "skill monkey" can be very useful. Song of Rest and Bardic Inspiration are also great party assets.
Long Term considerations
bards are often healers and usually lack meaningful offensive spells
Not in my experience. Our first 5e group had a College of Lore bard and a Tempest domain cleric. We never felt at a loss for offensive magic.
Lore Bards get significant benefits from magical secrets; they can hand pick any spell from any list to fill in offensive, control, or utility. Clerics get spirit guardians at level 5, already have guiding bolt and Inflict wounds at level 1, and get things like earthquake at level 15. (I've seen that spell wreck a frost giant stronghold.) A tempest cleric gets call lightning at level 5. If you have access to Xanathar's Guide to Everything, there are some more choices that you may want to add to their spell lists. If not, the PHB spells are still good enough.
Your whole group is on a journey of discovery; your players are the stars, not your plot.
Mechanical point: use short rests!
Pace the game so that the PCs can take advantage of the short rest recharge of various class features, to include the use of Hit Dice for healing.
See if you can find a fourth player
That may help round out your group in a different way.