Bendamustine and Idarubicin in Treating Older Patients With Previously Untreated AML or MDS

Inclusion Criteria: * Diagnosis of untreated AML or MDS with 10-19% marrow blasts; patients may be enrolled if they received prior treatment with demethylating agents specifically for the purpose of treating MDS or if they have received a single dose of cytarabine for the control of symptoms related to AML * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2 * Serum creatinine =\< 2.0 mg/dL; if serum creatinine \> 2.0 mg/dL, then the estimated glomerular filtration rate (GFR) must be \> 50 mL/min/1.73 m\^2 as calculated by the Modification of Diet in Renal Disease equation * Serum bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate transaminase (AST)/alanine transaminase (ALT) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x ULN * Capable of understanding the investigational nature, potential risks and benefits of the study, and able to provide valid informed consent * Males should be willing to use an effective contraceptive method during the study and for a minimum of 6 months after study treatment * Women must be postmenopausal or must be willing to use an acceptable method of contraception to avoid pregnancy for the entire period of the study and for at least 3 months after the study; a postmenopausal woman is defined as a woman who has experienced amenorrhea \> 12 consecutive months or a woman on hormone replacement therapy with documented follicle-stimulating hormone (FSH) level \> 35 mIU/mL; for patients in whom menopausal state is in question, a negative pregnancy test will be required prior to enrollment Exclusion Criteria: * Current concomitant chemotherapy, radiation therapy, or immunotherapy other than as specified in the protocol * Use of investigational agents within 30 days or any anticancer therapy within 2 weeks before study entry with the exception of hydroxyurea or single-dose cytarabine; subjects who are enrolled with high risk MDS (specifically) may have prior treatment with drugs in the class called "demethylating agents"; examples of these drugs include 5-azacytidine (azacitidine) and 5-azadeoxycytidine (decitabine), and may include approved or experimental drugs not currently used, which fall into this class and may be developed in the future; the patient must have recovered from all acute toxicities from any previous therapy * Have any other severe concurrent disease, or have a history of serious organ dysfunction or disease involving the heart, kidney, liver, or other organ system that may place the patient at undue risk to undergo treatment * Patients with a systemic fungal, bacterial, viral, or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment) * Pregnant or lactating patients * Any significant concurrent disease, illness, or psychiatric disorder that would compromise patient safety or compliance, interfere with consent, study participation, follow up, or interpretation of study results * Known hypersensitivity to bendamustine (bendamustine hydrochloride) or idarubicin * Clinical evidence suggestive of central nervous system (CNS) involvement with leukemia unless a lumbar puncture confirms the absence of leukemic blasts in the cerebrospinal fluid (CSF) * Have had a diagnosis of another malignancy, unless the patient has been disease-free for at least 3 years following the completion of curative intent therapy * Other circumstances in which patients with prior malignancies are not excluded, include the following: * Patients with treated non-melanoma skin cancer, in situ carcinoma, or cervical intraepithelial neoplasia, regardless of the disease-free duration, if definitive treatment for the condition has been completed * Patients with organ-confined prostate cancer with no evidence of recurrent or progressive disease based on prostate-specific antigen (PSA) values if hormonal therapy has been initiated, or a radical prostatectomy or definitive radiotherapy has been performed * Concurrent hormonal therapy is allowed