Singapore has an extensive public transit system. An average bus or MRT ride will cost between $1 and $2.25 SGD. The two closest MRT stations to Tanglin are Buona Vista and one-north.
The MRT system map is available here.
The SBS Transit app (Google Play | Apple) has up-to-date bus and MRT timings.
Taxi and Ride-share Apps
Taxis and ride-shares are generally reasonably affordable in Singapore, though post-pandemic, prices have risen (particularly at peak times or when it rains).
The ComfortDelGro (CDG Zig) app offers both taxis and ride-shares. (Google Play| Apple)
Grab is the most popular ride-share app. (Download)
Other ride-share options include TADA (Google Play | Apple) and Gojek (Google Play | Apple).