The recently discovered ATi
3
Bi
5
(A=Cs, Rb) exhibit intriguing quantum phenomena including superconductivity, electronic nematicity, and abundant topological states. ATi
3
Bi
5
present promising platforms for studying kagome superconductivity, band topology, and charge orders in parallel with AV
3
Sb
5
. In this work, we comprehensively analyze various properties of ATi
3
Bi
5
covering superconductivity under pressure and doping, band topology under pressure, thermal conductivity, heat capacity, electrical resistance, and spin Hall conductivity (SHC) using first-principles calculations. Calculated superconducting transition temperature (
T
c
) of CsTi
3
Bi
5
and RbTi
3
Bi
5
at ambient pressure are about 1.85 and 1.92 K. When subject to pressure,
T
c
of CsTi
3
Bi
5
exhibits a special valley and dome shape, which arises from quasi-two-dimensional compression to three-dimensional isotropic compression within the context of an overall decreasing trend. Furthermore,
T
c
of RbTi
3
Bi
5
can be effectively enhanced up to 3.09 K by tuning the kagome van Hove singularities (VHSs) and flat band through doping. Pressures can also induce abundant topological surface states at the Fermi energy (
E
F
) and tune VHSs across
E
F
. Additionally, our transport calculations are in excellent agreement with recent experiments, confirming the absence of charge density wave. Notably, SHC of CsTi
3
Bi
5
can reach up to 226
ℏ
·(e· Ω ·cm)
–1
at
E
F
. Our work provides a timely and detailed analysis of the rich physical properties for ATi
3
Bi
5
, offering valuable insights for further experimental verifications and investigations in this field.