This is an absolutely delightful Combo Deck. The goal from turn one is to set up a combo deck to kill everybody in one turn(ideally.) The following is a quick write-up for a few of the more important combos in the deck. Most of the rest of the cards are either tutors, wheel effects, or fast mana; all of which let you either churn through your deck or power out the combos.
Combos:
BomberMan: The name of the deck. The combo uses Auriok Salvagers and Lion's Eye Diamond to generate infinite mana. Sacrifice LED to generate three white mana. Use Auriok Salvagers' ability to return LED to your hand, using two of the three mana LED generated. Do this infinitely to generate infinite mana of every color. Your win condition with this combos are, Breya, Etherium Shaper, Pyrite Spellbomb, or Walking Ballista, all of which allow you to deal infinte damage to your opponent. Pyrite Spellbomb or Walking Ballista are good backups in case Breya, Etherium Shaper is somehow unusable. And the other spellbombs are in the deck to draw as many cards as it takes to find the kill piece while possibly generating an additional infinite effect if you, for some reason, are not able to draw as many cards as you'd like.
ThoperSword: The main pieces for this combo are Thopter Foundry and Sword of the Meek. Augments that can be used to improve this combo are Krark-Clan Ironworks, Urza, Lord High Artificer, or Time Sieve. Have Thopter Foundry and Sword of the Meek in play. Pay one mana to activate Thopter Foundry ability, sacrificing the Sword of the Meek. This generates a 1/1 thopter and gains you one life. Sword of the Meek sees a 1/1 token being created and returns itself from the graveyard and attaches itself to the token. This process can be repeated as many times as you have mana to activate. You can then go infinite if you have Krark-Clan Ironworks in play by sacrificing the token to Krark-Clan Ironworks to generate two colorless mana. This generates infinite colorless mana which can then be used to make an arbitrarily large number of 1/1 thopters. Urza, Lord High Artificer also allows you to go infinite by generating infinite blue mana and also allows you to cast your entire deck with said mana. You can also augment this with Time Sieve. You need to be able to go through at least five iterations of the combo and then sacrifice the tokens to Sieve to get an extra turn. With Extra turns, you can dig until you find a game ending combo of your choice.
Breya Displacer: The Combo pieces for this combo are Breya, Etherium Shaper, Eldrazi Displacer, and Krark-Clan Ironworks. Ashnod's Altar can also substitute in this combo as a replacement for Krark-Clan Ironworks. Have Eldrazi Displacer and Krark-Clan Ironworks in play. Put Breya, Etherium Shaper into play generating two tokens. Sacrifice the two tokens to Krark-Clan Ironworks generating 4 colorless mana. Use three of that colorless mana to flicker Breya, Etherium Shaper, generating two tokens on entry. Doing this nets you one colorless mana per iteration. After generating infinite mana; sacrifice the two tokens to Breya, Etherium Shaper to deal 3 damage to your opponent and then flicker Breya, Etherium Shaper. Infinite damage to each opponent.
Rings of BrightHearth: While not a combo by itself; this artifact allows for MANY infinites. The main ones are with Basalt Monolith or Sensei's Divining Top. If you have at least two additional mana to start; you tap Basalt Monolith to generate three mana. You then use that three mana to untap Basalt Monolith and copy the ability using Rings of Brighthearth by paying an additional two mana. This allows you to make a total of six mana, netting you one colorless mana for each iteration. The Sensei's Divining Top combo works similarly but is limited without the use of infinite mana. Tap Sensei's Divining Top to draw a card and then copy the ability with Rings of Brighthearth. This draws you one card from your library and also draws you the Sensei's Divining Top which you can then replay and loop.
Chromatic Orrery: Chromatic Orrery specifically combos with the creature Filigree Sages. Chromatic Orrery taps for five coloreless mana on its own, and has a static ability which allows you to spend any type of mana as any color of mana. This card is great on its own as it allows you to draw cards if needed, and it effectively acts like a super Chromatic Lantern. Filigree Sages comes into play with its activated ability. Since you can spend coloreless mana as though it were blue mana with Chromatic Orrery out, you can use the five mana it gives you to activate Filigree Sages, targeting Chromatic Orrery. This profits you two mana per iteration, and gives you infinite colorless mana, which can be used as man of any color. You can then use this mana to cast and activate Breya, Etherium Shaper, sacrificing herself as part of the cost.
Zirda: This is another card that's enabled several infinite mana loops. The static ability on Zirda, the Dawnwaker makes Basalt Monolith or Grim Monolith two mana cheaper to activate, regarding their untap abilities, which allows you to profit mana off their activated abilities. Much like Rings of Brighthearth before it, this can be used to generate infinite colorless mana which can be used in a variety of ways with this deck.
Builder's note: I designed this deck to be as competitive as possible. This obviously means I put the OG duals in the list as well as a number of other non-budget friendly cards. With this said; the only card over $100, at time of typing, that I feel this deck requires is Lion's Eye Diamond. Lion's Eye Diamond is pivotal to the central combo of the deck. The other cards of high value allow you to power out the deck faster of make your mana more reliable. This deck could easily operate at a lower budget and run a turn or two slower which may be fine in some play-groups. The main combos are central to the deck. The Tutors improve consistency but are not REQUIRED for the deck to operate. And the mana base can be tuned down to lower costs.