Does a citizen of Bangladesh need a visa in Bangkok if flying on separate tickets?

In your case, Thailand does not allow transit without visa for flights booked separately. So you need a visa and proof of funds, whether you have checked luggage or not.

For transit, Timatic states:

Visa

Visa required.

TWOV (Transit Without Visa):

Passengers transiting through Bangkok (DMK) arriving on Thai AirAsia (FD) or Thai AirAsia X (XJ) with a confirmed onward ticket for a flight on Thai AirAsia (FD) or Thai AirAsia X (XJ) to a third country within 24 hours. The connecting flight must be booked on the same ticket. They must stay in the international transit area of the airport and have documents required for the next destination.

Passengers transiting through Bangkok (BKK) with a confirmed onward ticket for a flight to a third country within 24 hours. The connecting flight must be booked on the same ticket. They must stay in the international transit area of the airport and have documents required for the next destination. Exception: This TWOV facility does not apply to passengers traveling on Air Busan (BX), Angkor Air (K6), Bamboo Air (QH), Beijing Capital Airlines (JD), Cebu Pacific (5J), Eaststar Jet (ZE), Go First (G8), Golden Myanmar Airlines (Y5), Greater Bay Airlines (HB), Hebei Airlines (NS), Indigo (6E), Jeju Air (7C), Jetstar Pacific (BL), Jin Air (LJ), Lanmei Airlines (LQ), Lao Central Airlines (LF), Lucky Air (8L), Mandara Airlines (RI), Norwegian Air (DY), Okay Airways (BK), Peach Air MM), Regent Air (RX), Salamair (OV), Scoot (TR), Shandong Airlines (SC), Shanghai Airlines (FM), Shenzhen Airlines (ZH), Siberia Airlines (S7), Sichuan Airlines (3U), South East Asian Airlines (DG), Spice Jet (SG) Spring Airlines (9C), Starlux Airlines (JX), Thai Air Asia X (XJ), Thai-Viet Jet Air (VZ), Tianjin Airlines (GS), Turkmenistan Airlines (T5), T'way Airlines (TW), Ural Airlines (U6), VietJet Air (VJ), Vietravel Airlines (VU) and Zipair Tokyo (ZG).

Passengers transiting through Phuket (HKT) with a confirmed onward ticket for a flight to a third country within 12 hours. The connecting flight must be booked on the same ticket. They must stay in the international transit area of the airport and have documents required for the next destination. Exception: This TWOV facility does not apply to passengers traveling on Air Busan (BX), Angkor Air (K6), Bamboo Air (QH), Beijing Capital Airlines (JD), Cebu Pacific (5J), Eaststar Jet (ZE), Go First (G8), Golden Myanmar Airlines (Y5), Greater Bay Airlines (HB), Hebei Airlines (NS), Indigo (6E), Jeju Air (7C), Jetstar Pacific (BL), Jin Air (LJ), Lanmei Airlines (LQ), Lao Central Airlines (LF), Lucky Air (8L), Mandara Airlines (RI), Norwegian Air (DY), Okay Airways (BK), Peach Air MM), Regent Air (RX), Salamair (OV), Scoot (TR), Shandong Airlines (SC), Shanghai Airlines (FM), Shenzhen Airlines (ZH), Siberia Airlines (S7), Sichuan Airlines (3U), South East Asian Airlines (DG), Spice Jet (SG) Spring Airlines (9C), Starlux Airlines (JX), Thai Air Asia X (XJ), Thai-Viet Jet Air (VZ), Tianjin Airlines (GS), Turkmenistan Airlines (T5), T'way Airlines (TW), Ural Airlines (U6), VietJet Air (VJ), Vietravel Airlines (VU) and Zipair Tokyo (ZG).

(Emphasis mine)

So transit is not possible without a visa.

The first airline will consider that your final destination is Thailand, in which case Timatic says:

Visa

Visa required.

Additional Information:

Visitors older than 12 years must have sufficient funds to cover their stay (at least THB 20,000.- per person or THB 40,000.- per family). Proof of funds includes Letters of Credit, vouchers, Miscellaneous Charges Orders (MCO) or credit cards accepted in Thailand.